I very much enjoy these kinds of games. I see most have already been mentioned, so I'll just add to this a bit.

I am not a Monster is a great parody of Star Trek: The Original Series and old, campy sci-fi flicks. This game is strictly humour, but it has some weird mechanics - like the turn's are instantenous for every character, which seems chaotic. You give out orders, and then everyone moves at the same time, so your orders might not get carried out properly or at all even. It's weird but you can get used to it.

Someone beat me to Shadow Watch. If you are looking for something more serious this game might be it. It has this serious covert ops/spy-thriller vibe, with a terrorist threat. Yes it's archaic, but still enjoyable enough to give it a try. But in this one you get a fixed team of agents.

Out of the above I only played XCom: Enemy Unknown. It's a very fun game, but also very flawed to my tastes. The RNG in this game is atrocious and infamous. Sometimes the game has already decided on the exact outcome of the mission - you just don't know it yet. Save scumming is not an option - if you did not hit the enemy with your 90% accuracy, you will never hit him in this round. The percentages in this game are bs. And it's not like the game won't find other ways of screwing with you. It's still fun, but extremely hard - you will have to learn and restart the game at least once, when you get how it operates! I think I liked XCom 2 much better - and that one is a bit more wacky, very much in style of the "V" miniseries.
I am very much interested in Phantom Doctrine but heard so many different opinions I'm not quite sure should i get it. It's on sale now, so maybe I'll chance it.

I do recommend Xenonauts though. This is an excellent copy of the original X-Com's, but with that indie/oldie style. I'm waiting for the second one already. For that matter you should try at least one original X-Com game (Ufo Defense; Terror from the Deep; Apocalypse ). They are quite similar but they differ in the details, so each one is it's own beast.

Now here are some, that were not mentioned, albeit mostly these are significantly less X-Com'ish:
1. Depth of Extinction - has a killer soundtrack and a very nice levelling system, great atmosphere too, but gets very repetitive fast.
2. Company of Crime - I don't know about that one... I like the setting (60's London), but it's not that dominant. You can play as a criminal or policemen, which is nice. Still it seems sluggish and a little boring (at least to me). I got confused when my hardened criminals got beat-up by some hairdressers and half my squad got arrested because of that. It has some nice ideas but struggles with them a bit. Definetly wait for a sale with that one
3. Chroma Squad - this one is significantly less X-Com'ish than the rest, but it's a fun tactical game nonetheless. One warning though. Only get into it if you are a fan of Tokusatsu shows or at least Saban's Power Rangers, as the game really works only on that humour and/or intertextuality. If you are a fan - this is gold. If not - you might not find it fun to play.

I'm not picky when it comes to games like these, it's one of my favourite combat mechanics/gameplay styles. It probably takes quite a lot for me to not like a game with these mechanics.

If I had to pick a favourite it would be the Shadowrun series.

I liked Xenonauts more than the Xcom reboots.

I did not like Stirring Abyss at first (wrote a negative review on it), but I re-bought it recently, and after the patches I now think it's a really cool game. Hard West was fun as well, and is quite cheap these days. I enjoyed Omerta as well.