You can play X-COM via DOSBox without any problems. The version on GoG is reliable and iirc comes with a preconfigured DOSBox frontend. You can also just extract the game files and run it on Linux if that's your platform right now, although I think that it had some extra strings attached.
I've wasted countless hours on X-COM and Terror From The Deep when I was younger.
That's what I do now when I'm certain that I have no plans or stuff to do for next eight hours or so. :P
I told you about it already, but the new XCOM is pretty good (and closer to the original game) with the Long War fan-made mod. Here's a bit of their FAQ that convinced me to give it a go:
Q: I'm fairly new to XCom. What difficulty should I start with?
Q: I'm an XCOM veteran. What difficulty should I start with?
Q: But I'm really awesome at --
A: Sorry to interrupt, but just start with Normal. We don't have easy difficulties in this mod that hold your hand while you learn the ropes and we've removed every bit of code we can find that cheats for the player on the lower difficulties. It's going to be hard. The other difficulties are just harder versions of Normal; feel free to move up when you get a handle on all the new mechanics.
EDIT: They didn't lie about that.
I'll have to try it someday. I heard almost exclusively good things about the game. Since we seem to have really similar taste in games, I'm taking that as a recommendation. :D