I know there's already one here, but hey! We could always use more. Feel free to yell at me about why I'm wrong.

Tier 0 - Virtually unbeatable. A step shy of PC Master Race.

Zulu (without x10 Wonders)
The best war power in the game, period. Not only do you not need to pay for having a large army, but the XP needed to promote a unit is now 0. This means that every unit starts with every promotion, and every time they battle, they can expend promotions to get their health right back. And when the Ikanda is up? Its promotions multiply by 10, too, so now your soldiers are having their stats multiplied by 400% or more, enjoying complete invulnerability to ranged attacks, and streaking across the map faster than most cavalry. Two starting warriors can take down entire nations. The only civs that stand anything resembling a chance against the Zulu with an Ikanda up are science-focused ones, which can either overpower their soldiers before they can regenerate or try nuking them, and even those had better be starting on a different continent. On one particularly stompy match, I decided to give the opponent I was fighting a Giant Death Robot through the ingame editor - one suffering from resource penalty because it was the Medieval Era, but still - and it got ripped apart inside of two turns by Impi. Do not play against Zulu.

Tier 1 - Leagues ahead of other civs. Functionally limitless and able to abuse things nobody else can even touch. The only ones with a chance of defeating the Zulu.

Babylon
Ten free Great Scientists with Writing and 500% production on them from then on. With Babylon, you can pretty much instantly skip ahead to the Medieval Era. The old joke on Babylon is that they have stealth bombers when you have muskets, and this can be literally true. Plus, the Walls of Babylon get multiplied too, making their cities basically invincible. Probably the closest thing to a Zulu counter.

Korea
The other broken science-focused civ. +20 science for every Specialist and a colossal tech boost mean that Korea is, as ever, actually a bit faster than Babylon once it gets rolling. If it had a unique building, I'd call it better.

Egypt
Triple-speed Wonder construction, in a mod where every wonder is supercharged. Since this includes the Great Library, Egypt can actually hold its own against science-focused civs by grabbing ten free techs. What's more, this is available from the beginning, and once you've built one, it's very easy to snowball. Petra, Big Ben, and Angkor Wat in particular will break the game. The +20 Happiness for Burial Tombs is just gravy.

Zulu (with x10 Wonders)
Yes, the Zulu get two listings - and it's only because a handful of Wonders are so good that it gives a few civs a chance against them, while the Zulu don't have enough production to build them first. Particular ones include the Red Fort and Himeji Castle, which make cities so borderline invincible that even the Zulu can't feasibly conquer them. This still requires a lot of luck and possibly starting on a different continent, since most of those Wonders show up later on, but if it happens, it gives all civs a possible counter against the Zulu.

Tier 2 - Functionally unlimited in some manner, but the thing they're good at isn't as amazing as the Tier 1s. Usually involves some kind of boost to food or hammers.

Spain (with a Natural Wonder)
You know how Spain in the base game gets kinda broken with a Wonder? Well, just multiply that. The increased gold bonus will give you enough money to buy anything, the x20 stat for a Wonder will instantly turn your city into a powerhouse. Just for some idea: El Dorado gives you 10,000 gold if you find it first. Spain with Great Barrier Reef is pretty much Tier 1, as they'll be enjoying a +80 Science. You still have to get there, though.

America
+10 Sight means that you explore the entire map inside the Ancient Era. Reduced cost on buying tiles turns into getting massive amounts of dosh for buying tiles. Every single city turns into a colossal windfall. It's trivially easy to own most of the continent, and buy all the buildings in every single one of those cities. Plus, between seeing everything and having giant piles of money, you can instantly ally with every city-state.

Russia
The Krepost lets you steal half of America's unique ability, and we know how broken that is. Every strategic resource is now making more production than a manufactory. And you pretty much never have to worry about oil, iron, horses, or uranium ever again. They may not be able to do it straightaway and they may not make quite as much dosh off it, but they can hold their own against America.

Inca
Terrace farms. +10 Food terrace farms. You have so much food that your only worry ought to be overpopulation, and you're actually getting paid for maintenance. By the Classical Era, you should have more population than everyone else put together.

Tier 3 - Terrifyingly powerful, but not unlimited in the fashion of the Tier 2s or takes a while to get there.

Ethiopia
As ever, instant religion. As in, pantheon on turn 9, Great Prophet on turn 20, and reformed belief not long after. Your units get tripled strength while fighting enemies with more cities, which should speak for itself. Another potential Zulu counter, limited only by the fact that religion isn't as meaningful in x10.

China
You can make Great Generals pretty much whenever your units so much as sneeze, and they nearly quadruple the strength of the units around them. The massive pile of extra gold from Paper Makers can come in handy, too. It's only their lack of infrastructure buffs that keep them out of Tier 2.

Poland
Ten social policies for every era. Instantly fill out a tree every time you enter another era, with room to spare. This happens so fast that it's advised that you turn on Save Policies, since otherwise you'll quickly get stuck from running out of stuff to buy. The Ducal Stable turns Pastures into a +10 gold buff, and makes all your mounted units into war gods. As ever, Poland's just really good.

Huns
+10 to Pastures is a pretty gigantic boost, and it comes almost right away. The Hun early game is as good as ever; only the fact that most Tier 2s can do something similar or better keep it out of there. Also, the ability to roast a city in one turn is pretty cool.

Morocco
If the Kasbah came online earlier, Morocco would easily be Tier 2, and once it shows up, they're likely there - but it doesn't. The +10 Culture boost for trade routes is great, but the gold boost is, as ever, a bit of a two-edged sword. And while +10 Culture certainly sounds like a lot, the way Culture scales means that you won't be able to grab as many social policies as you'd think (still a lot, mind).

Maya
The worst of the science-focused civs, since Long Count doesn't multiply. But a +20 Science boost for every Temple is still a gigantic boost, and that's enough to move them here.

Aztec
Inca but clumsier. The culture-on-kills being multiplied is enough to basically fill out an entire tree in the first few turns. But the real love, of course, is the Floating Gardens doubling the growth rate of all your cities and turning lakes into spawning grounds.

Tier 4: Considerably above the base-game civs, but their advantages are harder to leverage compared to the Tier 3s, especially against their fellows.

Iroquois
Probably the weakest of the infrastructure-buffers, simply because the Longhouse takes comparatively long to show up and only provides a +10 to hammers with forests. But hey, giant production boosts are giant production boosts.

Netherlands
The other infrastructure-buffer in Tier 4. Polders are great when they show up, but marsh is rare and polders show up late. Aside from that, you gain Happiness for trading away luxuries, which is funny but not super useful.

Arabia
The Bazaar gives you phenomenal amounts of gold, your trade routes are basically Great Prophets, and you have more oil than exists on the planet. That said, your gold is "very, very good", not "unlimited", and even then, it's restricted to certain resources.

England
Your naval units might as well be on rocket engines, making exploring the entire planet quite easy. Dedicated naval civs still give trouble, though. Those ten extra spies are hilarious, even if you do run into diminishing returns a fair bit on spies. But you'll have a lot of tech to steal and a lot of city-states to rig, and England is already good.

France
The multiplied theming bonus may not sound like much, but cultural victory is an every-point-counts game. The Chateau takes a while to show up, but when it does, France basically becomes a demi-Poland. The only problem is that cultural victory isn't as good when some people have insane culture growth and others have nukes.

Celts
Take what I said about Ethiopia, remove the combat bonus. +10 Faith from the start is pretty hilarious, even if Religion is something of a drop in the bucket in x10, and it'll get you a pantheon by the second turn. +30 Happiness is about as high as you'll go without a Wonder, so conquest, if you can manage it, is no problem.

Persia
Even if a +20% to production and culture and +1 gold isn't as much as its fellows, once that Golden Age gets going, it will basically never end, and Persia's units become twice as strong and superfast. Once banks are online, you never have to worry about happiness or money again. Getting to that Golden Age before someone else kills you is the only problem.

Brazil
The other good Culture civ; their tourism bonus multiplies by eleven during Carnival. If you have any Tourism at all, this should get you most of the way there. Not unlike France, the Brazilwood Camp is nutty. But Brazil has a slow start, which is painful in x10.

Germany
Barbarian units join you almost instantly and give you a good pile of gold, and your troops work pro bono. Handy in the early game, but where they come online is the Hanse, which has its production boost upped from 5% to 50% - per trade route. It'll take a while, but when it's there, Germany goes crazy.

Portugal
Another gold-maker. Not much to say here, the Mare Clausum should have you rolling in cash pretty quickly.

Shoshone
The coolest part of playing Shoshone is plonking down a new city and seeing half the map turn grey and blue. Your giant friendly-lands combat boost means you should be able to easily slaughter the people annoyed at your newfound eighty tiles. But... you don't need eighty tiles, especially when you can only work a handful of them.

Siam
Your city-state friends provide some big rewards, but you still have to get there first. The Wat and its +30 Culture is great, but being a university means it comes a bit too late.

Songhai
You get a lot of early gold for barbarian-hunting, and capturing a city will basically ensure you never have to worry about money again. The Mud Pyramid Mosque is a culture-buffer, and it's early. But conquering a city in itself isn't easy.

Tier 5: Not much above the base game civs; their advantages are either impractical or situational, even if they might have a big number or two. Would probably lose to top-tier civs in the base game.

Venice
Everyone's favorite jerk. Having up to 200 trade routes is hilarious, but other civs can get to high money without needing to protect 200 trade routes (or build 200 trade routes, or figure out where 200 trade routes are heading to in a standard-size game). Also, you're Venice. Those ten Merchants are fun, though.

Rome
Not a good day for Italy; the Roman production boost for buildings outside the capital doesn't really add up to much when every other civ has either gigantic production boosts everywhere or giant piles of money to buy the buildings instantly. It's still handy, though.

Sweden
Even if it's pretty much going to last forever, one city-state ally for the price of a Great Person was pretty much just okay in the base game. The doubled Great Person rate is helpful, but the other side gets it, too.

Indonesia
You get a big Faith building and a buttload of luxury resources, and that's about it. The chief problem is that your building doesn't help you with actually founding a religion. And while having lots of luxuries is nice, outside of trading it ultimately doesn't give you anything besides Happiness, and Happiness doesn't need to be that high.

Greece
Your city-state alliances will pretty much never end and you can demand tribute at will, but everyone else has a giant pile of money. Want those alliances? Good luck.

Mongolia
You're in this for the speed boost on mounted units. Yeah, you can conquer city-states with a scout, but doing so is going to attract the attention of everyone else, who are probably a lot stronger than you. A speed boost is fine, but when half your neighbors have doubled power, it's not as good as it looks.

Assyria
Yes, you get ten free techs. If you were ten techs behind an opponent, you probably weren't going to be conquering anything of theirs. More likely, you'll get two, tops. The actual advantage is in the Royal Library, which, when filled, gives a beefy +100 XP. It's a bit tricky to fill in the early game, but pulling it off can give you a decent army.

Egypt (without x10 Wonders)
A pretty common rule for those who don't want the game to be a race to grab one of the many broken Wonders, and Egypt suffers particularly. Unless it grabs every Wonder in the base game, it's not going to beat most Tier 3 or even Tier 4 civs. And even then, its lack of production boosts elsewhere means that civs with infrastructure boosts can outrun Egypt at its own game.

Tier 6: No better than high-tier or mid-tier civs in the base game. In extreme cases, may be no different from what they once were.

Spain (can't get a Wonder in its territory or find any Wonders first)
Well, you get more extra gold for finding them second, and extra Happiness. That's it. Good luck.

Austria
The Coffee House is your only buff here, and it doesn't show up for a good while. You'll get a big pile of Great People, but by that point, you've been conquered and bulldozed.

Denmark
Your Embarked units are super fast. Fast Embarked units are not going to win the game.

Polynesia
Weirdly, two of Polynesia's traits aren't multiplied; they don't get +10 sight from embarked units, and they don't get +10 Culture from Moai. They do get +10 Gold when Flight happens... but that's Flight. You are not going to be winning off +10 Gold from Flight.

Ottoman
You don't have to pay for your fleet anymore, but you weren't paying much for it to begin with. You have a higher chance to grab barbarian ships, but your chance was already very high. It's only the extra starting gold that actually matters.

Japan
A subpar civ to begin with, their sole advantage only comes into play with a somewhat specific resource you might not be starting next to, and dozens of civs have +10 Culture routes.

Byzantium
Well, it had to hit somebody; Byzantium has literally no advantages over the base game. And it's not like Byzantium was anything to write home about.

Carthage
The description says Carthage gets ten free Harbors. The description lies; it gets one, like the regular game. This means Carthage is unchanged. And like Byzantium, it wasn't great to begin with.

Tier 7: India.

Imagine being Gandhi. You lead a group of one thousand settlers in 4000 BCE, and finally locate a place by a river, surrounded by plains and trees, and begin building the houses that will be the beginnings of Delhi. You look forward to teaching the other leaders about the ways of peace and the power of the atom. The moment the last house of the settlement is finished being built, every single person there begins complaining. The soldiers don't want to fight, the scholars don't want to study, nobody is farming or having sex.

Before long, you hear talk of rebellion, and sure enough, less than two centuries in, the discontented peoples raise in revolt, and lay siege to the settlement of Delhi, which has not grown in the slightest since its founding. The revolts continue for millennia as they try to burn their new home to the ground. You teach your people codes of honor, that they may hold firm against the deserters. You hope that your people are fraternal, and that when the city will grow larger, it may remember its kindness.

Other settlements encounter you. They distrust you, for your people dislike you so. The only thing keeping you alive is that the river separates you from the rebels. Before long, they join up with the native barbarian tribes, and you are besieged on two fronts. Your long-suffering spearmen battalion, outnumbered three to one and shellshocked, falls at a thousand cuts. Eventually, the archers from the walls of your city slaughter enough barbarians for you to learn the art of the Landed Elite, and a small caste of your society begins to distribute the food, finally raising your population growth above stagnation - but only barely.

Around 500 BCE, your population finally rises to 6000. You send out a worker, in the hopes of taking one of the luxuries surrounding you. They are instantly taken by a neighboring tribe. Around you, you see your enemies and rivals advance, their swords forged from iron and steel. One of them invades you; somehow, you repel them, but in the chaos, the rebels rob your treasury, leaving your already barren scholars unpaid.

Around 1000 AD, you manage to protect a worker long enough to connect valuable resources, and so the revolt comes to a close. A few centuries later, you manage to finally raise your approval above 50%, and your population begins to blossom... and then you finally look outside at your peers again and realize you are on the level they were on three thousand years ago. You may have nowhere to go but up, but you will have to go up very fast, with your... +20 Culture and Tourism Mughal Fort.

For note, on Prince difficulty, you start with 9 base Happiness, which India's penalty drops to -20. On the lowest difficulty levels, your base Happiness is high enough for it to not be a worry... but if you're playing a x10 mod on the lowest difficulty, may I suggest you turn off Civ V and instead go play a game more your speed, like Candyland.