I don't seem to have this problem.
There might be corrupt files or something scattered around the game folder.
This probably won't help you, but I suggest you delete the current folder (copy the one with your saves) then download a fresh copy of the game and extract it.
If that doesn't work, the next problem might be corrupted save games.
Either that or there's some other problem that's conflicting with your PC.
When it crashes, does it go to a black screen? Or quit to the desktop?
Try the above, and if it doesn't work, there are some gurus here that can most likely solve your problem.
EDIT: There seems to be another person with the same problem, check out this thread.
X-COM CRASHING