PSA for anyone having trouble like me. I had crashing issues with two computers, one a modern gaming desktop with a Geforce 770, the other a laptop with Intel IGP graphics. The desktop would randomly task switch to my desktop (especially when starting the game), leaving the game in an unresponsive state that can only be killed with the task manager. On the laptop it just plain crashes.

One of the commonly suggested remedies is to disable movies, and for me this worked, but I find that solution unacceptable. I found a better solution that lets you keep the FMVs.

Before I explain how, you might want to disable the intro logo movies anyway. You can do this by:
Go into the game directory
Open the folder "movies"
Delete these three files: "biologo.bik" - ""leclogo.bik" - "legal.bik"

Now, to enable windowed mode, find a file in the game directory, "swkotor.ini." Open it, find the section with "[Graphics Options]". Make it look like this:

[Graphics Options]
V-Sync=1
Anisotropy=1
Frame Buffer=1
Anti Aliasing=0
Texture Quality=2
Emitters=1
Grass=1
Soft Shadows=0
Shadows=1
Brightness=57
EnableHardwareMouse=1
FullScreen=0
Disable Vertex Buffer Objects=1
RefreshRate=60
Width=800
Height=600
AllowWindowedMode=1

The important parts here are these:
FullScreen=0
Disable Vertex Buffer Objects=1
AllowWindowedMode=1

You will probably have to add that last line yourself.

Once I did that, the game worked perfectly, on both of my computers. FMVs worked fine, though on the desktop it will occasionally task switch after an FMV, but no big deal - now I can actually task switch right back and resume the game without trouble.

And if you don't want to play the game in windowed mode all the time? No problem. Just press Alt+Enter ingame to switch to fullscreen. Just be sure to switch back to windowed mode with another Alt+Enter before any FMV scene (such as when traveling in the Ebon Hawk).