Wowee, this is something I need to magic up a fortnight for. Since 2009, the OpenXcom project has been unhurriedly continuing in its quest to make the original X-COM more contemporaneous, - a standalone version that doesn't require DOSBox, that makes the interface a little more modern, that offers more rule-tweaking for those that want it, that finally kills some of the bugs which have dogged the original for the past two decades, and even one that scales up to mega-resolutions impressively convincingly. As of the new version 0.9, it's basically got everything working, and you basically get an in theory improved, but faithful, X-COM to play right now.
The main draw is that the thing just runs, and the fixing of legacy issues such as "No more 80-item-limit, personnel limits, funding overflows, disconnected facilities, broken proximity grenades, floating soldier." If you load up OpenXcom, you're not going to notice much in the way of obvious change, bar some new options in Settings. Dig a little deeper and you might notice that the controls are more contemporaneous, in a way that you probably didn't even notice was happening. (Until the issue I keep hitting where scrolling on the keyboard tries to go in a random direction, anyway.) Then you might start noticing a few of the many little things listed here.
Is it to the game's benefit? I haven't been able to look at it for more than a few minutes as yet, but knee-jerk impression is very much yes. It's X-COM that basically runs and responds a little better, as far as I can tell.
While OpenXcom itself is free, you will need data files from the original game in order to play a game. If you don't already own X-COM in some form, I'm afraid we can't be friends. It's very easy to obtain now, via the Steams and GoGs and things, though I don't believe any proceeds go the game's original creators, depressingly.
Is OpenXcom's use of these assets legal? "It’s kind of a grey area," writes OpenXcom's creator. "I contacted the copyright holders just to be sure but they never replied back, so I’m just playing it safe like every other remake." But has he asked Julian Gollop? He's on twitter now, you know.