Also known as "The original X-COM", or the king of strategy games. The intro consists of a general "aliens are coming to kill us, but we will fight back with your commanding skills" plot, and then you are dropped into the world view to figure things out. Preferably before all of us are dead.
Play it for free in your browser, preferable Chrome, at Classic Reload.
Or dowload a pre-packed DOS box version.
Or a later version: X-COM Apocalypse.
SpecsUpdate
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Pros
Pro Very deep strategy
Keeping track of more than a dozen soldiers with 10 skills, their inventories (including ammo count and weight), dynamic visibility, line of sight, destructible terrain, consequences of missed shots (like friendly fire or destroyed loot), etc. quickly overwhelms noobies, putting the real strategy masters in the limelight. And this is just a battle out of many, with base building, personell management, logistics, reconnaissance, research and manufacturing between them.
Pro Active open source clone
The openxcom team have re-implemented the entire game and fixed many of the longstanding bugs in the original. It allows you to play on modern machines and in much higher resolution. A copy of the original game is still required for the assets.
Pro Dark humor
Seems to have started the "evil aliens" trend.
Cons
Con Artwork
The artwork is not to everyone's liking.