A person at worked tipped me off to a modern game that was very similar to X-COM: Enemy Unknown (UFO Defense in the U.S.). It's actually a Russian game from a developer called Chaos Concepts. The game is called UFO Extraterrestrials.
Before I actually played the game I read about it and it seems there are a few mods for it. One is called "Bman's ease of use mod 4.07 (fixed by Coasty)" and what this mod does is make the game even more similar to the original X-COM game. I've never played the true game, and instead elected to play with this mod installed from the get-go.
It's phenomenal. Very true to the original game with just a few differences. The nicest part is that it's a 2007 game and I've verified it runs fine on Windows Vista x64, so you get nicer visuals combined with ease of use. Compare that to the original X-COM where your best option is to try to track down the old DOS version to run in DOSbox (the Windows 95 version will run in Windows XP with a special EXE file, but will not run in Vista at all).
I highly recommend checking it out. It's just under $20 at Gogamer. It's also available in the underworld, but it's a weird version where the installer is in Russian but it's actually an English game.