Oh man, so many fond memories I remember playing it on my Amiga 500 Obviously also multiple times on the PC afterwards... It was called UFO: Enemy Unknown here. Can't beat free, but you can always get it cheap on gog.com too (with all the DOS Box setup included and whatnot). A true classic that's still fun to play today The sequel X-COM: Terror from the deep was also a lot of fun and a bit more brutal than the first game. And then there's X-COM: Apocalypse... I was one of the people who really enjoyed it (but that's not something universal, like for the first game).
Highly recommended Once you get sucked in, you'll really get into it.
It has an atmosphere in the missions that the new one just doesn't have. I remember being terrified on night missions especially when one of your guys gets taken out before hitting the bottom of the ramp and you can't see where the shots are coming from. Then you barely escape with one soldier that is half insane after the entire squad turned on each other while still inside the Sky Ranger. And finally in later missions the expertly launch blaster bomb that would path into your ship on round one scattering bodies all over the place. So many memories of this game.