I spent a good amount of my youth passionately playing video games...so here's an entire article
1. Deus Ex. My God, that was a game! It happened so many times - a cool scene randomly appears in my mind and I start thinking about which game/movie it was from. And it turns out to be from Deus Ex. And it had some of the coolest scenes EVER, the first encounter with the "men in black" probably being THE coolest. To top that, I was in Venice last year and the first thing that came to mind when I looked at the bridges & canals was "bah, seen it before...in Deus Ex"

. I cried when I saw the god damn awful, retard friendly abomination going by the name Deus Ex 2.
2. Unreal Tournament. I've played it since the demo came out and was decent at it. Had my share of first places in online games. Always prefered it to darker, slower Quake 3.
3. Planescape Torment. Awesome story, deep as fuck, awesome universe. Man wakes up in the mortuary without memories, finds out that he's immortal, has died numerous times before and is probably some kind of a deity.
New York Times said:
Is it possible for a computer game to have the intellectual heft and emotional impact of a good book while remaining as captivating as a well-paced film? If so, the first candidate may well be Planescape: Torment.
source:
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4. Fallout 2. Older than Planescape Torment, similar in style. Postapocaliptic world, Mad Max atmosphere, epic.
5. Warcraft 3. No introduction needed, best rts of all times. I pretty much suck at it compared to my
gosu friends, but can win a game or two online. It also holds one of my records - I played it for 18 hours straight a few weeks ago, from 22h 'till 18h tomorrow

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Honorary mentions go to Halflife, Master Of Orion 2, Fragile Allegiance, System Shock 2, Theme Hospital, Dungeon Keeper...