I was reading through some old Games for Windows magazines I got for free and found a quick blurb on UFO: Alien Invasion. It's an open source game based on X-Com. The site is here: http://www.ufoai.net/
I've put in 5-10 hours with it and it's pretty good. Somewhere on the site, they mentioned wanting to improve X-Com not just remake it with nice graphics. So far, that doesn't really seem to be the case. As far as I can tell it's just a redone X-Com with some different aliens, weapons, interface etc. It's somewhat hard to figure out how to do certain things or what things mean, and the manual that comes with the game fails to help much and seems to be made for an older version. Overall, it lacks the polish you would expect (but not always get) from a professional company. Still, if you liked the old X-Com you should have little trouble just jumping in and killing aliens. It's a fun homage to the original and you can't beat the price.