This is weird: I know what is number #1. Easily. The thing is, what the hell do I put in #2 - #5 spots.
(Could make a thread about games, which had the most impact on player. Maybe some other day.)
Oh well. Let's give it a shot, eh?
#5: Tropico 4
It's more about the charm of the game. Yes, I want to buy myself an island become El Presidente myself in real life. Despite repeats itself sometimes, I like how I can customize my Presidente as I want and how I can be total bastard if I want. This spot could've been occupied by Pharaoh as well, but chose Tropico for now.
#4: Battlefield 2
If you ask me, it's one of the finest, if not best FPS for me. Only thing which darkens my mind is air force of the game, but that is little compared how tight gameplay is, squad & commander system works very well, levels are big and wide and how goddamn enjoyable game is overall.
#3: DotA 2 (WC3 DotA)
How much can man hate a game? From how your teammates are bad, how enemy flames you for being bad, how that lucky critical strike decided to kill you instantly and how your Multicast never procs on Ogre Magi. Yet besides that, you shallow your anger and give it another go. And again and again. So no matter how much you hate the game, you play it and briefly, you enjoy it.
#2: Team Fortress 2
Battlefield 2 is probably the best FPS game for me. But it gets overshadowed how I've played TF2. From May 2009, I still pick it (although rather rarely lately) and give it a round or two. It also has introduced me to the Internet communities, meeting good people from aboard and playing with them many years. Friendships, which has lasted.
And even without the community effect on me, game is good itself, don't you dare say otherwise!
#1: Fallout 2 (Fallout/Fallout New Vegas)
In the end, there can be only one. Fallout had technically better story (and far better antagonist), while New Vegas was a godsend after Fallout 3 (which I personally don't like much). Yet, if there can be only one, it'd be Fallout 2.
Despite I finished older Fallouts with walkthrough, I enjoyed them intensively. They were excellent RPGs, despite I didn't figure out stuff myself. The atmosphere, the setting and the mechanics (especially SPECIAL. I'm just very fond of that). Game which taught me to listen Jazz. Game, which represents the best in gaming.
Fallout 2 was bigger, badder version of first one. Despite not as dark and much more tongue-in-cheek humor and references, it improved vastly the first game. No time limit (well there was but it took YEARS), more content, more guns, more quests and more tricks how to be overpowered from level 1 onwards. Just perfect. My favorite game (series)
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Some special mentions: Hotline Miami, Natural Selection 2, XCOM: Enemy Unknown (the reboot), FTL, Bioshock series (would've prolly fitted in the list), The Binding of Isaac, Atom Zombie Smasher, Borderlands, Men of War: Assault Squad, Sam and Max' (the Telltale ones), Rayman Origins and Metro 2033. More or less.
Oh wow, this was a chore to write. Hope you could skim through this, nevertheless.