Jedi Knight would launch in a window, and when I would try to start a game, it would play the introduction in a window... but after loading the level itself, the game would crash to the desktop.

Here's how I got it working:

Go to JK Hub at the link below and download the file named "jkultimate15.zip"

JK/MotS Ultimate Patches[jkhub.net]

Open your game folder in your Windows program files at:
.../Steam/steamapps/common/Star Wars Jedi Knight

Copy all of the contents of the jkultimate15.zip file into this folder, overwriting the original files.

Run the game, go to Options/Display, check the 3D acceleration box and choose your resolution.

After this, for me at least, the game works as expected.

(I'm posting this in February 2015 after getting this game in the Humble Bundle. I spent a lot of time trying other solutions posted here that did not solve this problem for me; hope this works for you too.)