If you have played the original X-Com from 15 years ago, you are spoiled for life. If you have never never played this original then any of the recent x-com titles, like UFO Aftermath or Afterlight are perfectly acceptable higher res, bertter sound, etc, xcom games. The problem is they are always compared with the original X-Com, which to be honest, I don't think any new game will match to it because no developer would release a hardcore PC game like this anymore!
When you think of how insipid and shallow most games are now, in terms of story, characterization, gameplay quality and amount of gameplay, an X-Com Unkown game, with it's sophistication and IQ required gaming will never be released again by a mainstream publisher!

The only one which is 'new', and that's at a stretch, is Enforcer. This game is not an object lesson in how not to do X-com games. Its an object lesson in how not to do shallow third-person shooters. If you take X-com out of the title, its tolerable in small doses if you are extremely bored.
Next down the line is Interceptor. This has not aged at all well. The strategic aspect of the game is still strong, but the flight engine .. they really should have paid more attention to what the competition was doing. Its far too fast, maneuvering is awkward .. but I remember it being better back in the old days, so perhaps its simply bugged on modern systems in even more ways than you will find described on forums. Notably, this has not been fixed in the Steam re-release despite it being certified as working in Vista - you cannot do probes or pirate base missions without cheats.
Now. The good stuff. X-Com Apocalypse is awesome, but its not the originals. Its all very competent, but the new aliens are .. well, they are not sectoids and ethereals. Still well worth your time and money though.
X-com Terror From The Deep is essentialy X-Com UFO defence part two. Some improvements have been made. The aliens are partly derived from the original and partly from Lovecraft. (Yeah, that Lovecraft. Elder Gods, Cthulu and all that). So far, so awesome. The down side is that there are some nasty bugs in the research tree (Fixable with a HEX editor if you have the needed data. At need, I can figure it all out again, just as soon as Valve start providing the DOS version of TFTD.). Also, the two part missions begin to become a chore, particularly the cruise ship terror sites.
And the original. X-COM UFO Defence. Or UFO: Enemy Unknown in Europe. Awesome. There are no flaws.

Well, you can add it to steam, like it was mentioned, but like all DOS games on steam they come with a preconfigured DOSBOX that they tested to run on vista/xp/whatever. Only certain games can be added to steam to be able to download/redownload, and those are mostly Valve games and a small handful of others.

I have played almost all the UFO/X-COM games (this includes Interceptor, which I want a competent remake of :p) and "sequels". While I can't comment on Alien Invasion (the last time I played it, it was barely a proof of concept), I can comment on most of the others.
I am going to ignore the actual X-COM games, since most people will either love the original (and bitch about 2 and 3 :p), or bitch about the graphics. And honestly, I don't blame them. It is hard to get into a game that isn't visually stimulating. Take Daggerfall for example. I know I will love it, but I just can't get started (but I still play Wizardry 2 on a regular basis...). Plus, everyone else already covered those.
There are two real branches of "sequels":
[url=]http://en.wikipedia.org/wiki/UFO:_Aftermath[/url]
There are the After*s (Aftermath, Aftershock, and Afterlight, I think). I enjoyed the first one, albeit it never really felt X-COMy outside of the subject material. Apparently the latter two are even less X-COMy (plus, they seem to work upon the premise that you failed miserably in the previous game...). The After*s seem to focus more on tactical combat, with research and base management a minigame (especially since gear is mostly found).
[url=]http://en.wikipedia.org/wiki/UFO:_Extraterrestrials[/url]
The second branch is UFO: Extraterrestrials. Not a well know game (but available in most stores), the only complaints I have heard about it is that it is too similar to the original X-COM. You WILL have casualties, and it is pretty difficult, even on the lowest difficulty setting. Hell, nothing beats arriving at a crash site and having your team slaughtered while they are still in the dropship :p. ET has a very strong emphasis on research and base management, and it takes quite a while before the player feels as though he or she stands a chance at survival. Plus, there are mods (BMan's comes to mind) that even add in the original X-COM sprites and enemies (touched-up a bit, I think).
So if you don't mind paying money, UFO: Extraterrestrials (with BMan's mod) is the truest sequel to X-COM out there. Honestly, the only UFO/XCOM games that really make me tingle (down there...) are the original and ET. They manage to truly capture the feeling of being completely (and utterly) boned. Of course, your mileage may vary.

Good point about the destructible environments. They were very much a part of the original game. If you cause too many fires, your guys pass out from the smoke or even die. Same with aliens. If you blast holes in the wrong place in the floor or ceiling, aliens can shoot you through them and vice versa. Or you can fall through them and get hurt. Or you can find a place unnavigable and have to take a longer and more dangerous route.
Plus the carnage was pretty cool!

I have, again and again, tried various 'remakes' of X-COM. Each time I come away a little disappointed with either the fact that the animations involved with the tactical aspect are too "smooth" or "slow" to really give it the chess feel that the original gave me, or they pus the "Real-Time" stuff so hard that you don't get a choice in the matter.
Overall, if someone were to ask me "What is the best most recent good version of X-Com", I'd still have to point to the original, even (as said before) now that Steam has it available legally through Dosbox, and let me tell you, even though it's stretched at 1680x1050, I think it looks perfectly fine for what it is.

Cept the Steam ones don't run on vista....

Um. Yes. Yes, they do. Except for TFTD, but they are working on replacing that with the DOS version wrapped with DOSbox - it takes longer than you might think to do this due to the need for two companies to coordinate, and quality assurance procedures must be followed, etc. But it cant be too much longer.
And of course Interceptor is still fatally bugged on anything more recent than win98, but theres nothing to be done about that short of reverse engineering the binary.

Pretty much what Andrewas just said. 2K's been busy moving TFTD to Dosbox lately, though we haven't heard any news of it for the past couple of days.
Every other one (excluding Enforcer) is based on Dosbox already, if I recall. That decision was made specifically for vista support.

Ok, granted.
When I looked at them when they first came out on steam they weren't.
I would still prefer them on GoG :D

Ok, ok I was wrong :D

Despite the new graphics it can still run on really low spec systems. I'm not even sure if there are any improvments beyond a slightly better interface either.

X-Com does need some improvements, mainly on the technical end. Also it would be nice if some of the weapons were useful cause once you get Lasers and then Heavy Plasma it's goodbye to everything else. Unless of course you're gonna only use Blaster Bombs. :P

Isn't that the point of adapting to alien tech? :P