Deus Ex (no, not Human Revolution. What the hell is wrong with you?).
Back in 2000 this game was a near revolution (system shock 2 did the same thing, more or less, but nowhere near as well) successfully mixing FPS, RPG and stealth gameplay with a very strong story, very well designed levels, interesting and reasonably well developed characters (I'm looking at you, mercs from human revolution) and very good gameplay.
Following the likes of Quake and Half-Life (which is a fantastic FPS, don't get me wrong, but not much else), You had an FPS where shooting an opponent in the back of the neck is better than shooting them in the head (hey, those helmets help apparently), where being a novice marksman meant that your sniper rifle wavers all over the place, but mastering it meant that you could shoot the nipples off an MiB from 100 paces (well, the tech was a bit too weak to render individual nipples, but you get my point), where getting shot in the leg meant you moved slower and getting shot in the arm meant your weapon wavered more and getting shot in the head was pretty much a guaranteed death (if you played it on realistic), where you had to make tough decisions about what gear to carry with you because, hey, you aren't a freaking truck on legs (but still gave you the option to be armed to the teeth if that was your thing), with levels that allowed you to go in guns blazing or sneaking unseen with enough exploration that, even many playthroughs in, I still found new stuff.
With choices that are in no way obvious, but are still acknowledged by the game if you make them: like entirely avoiding a bossfight by killing the character involved long before they are an enemy, and then blaming it on crossfire or completely changing the fate of a pivotal character by going against the odds in a near-suicidal attempt to save him or even running away from bossfights entirely. Or even walking into the ladies room at the office and being chided by your boss for doing so (which is entirely optional. There's no reason to go in there, other than to explore).
With a fantastic (if formulaic) story and levels that reward exploration far beyond the occasional loot piece or discarded food item - heck, you could miss entire plotlines and characters. In fact one of the more interesting characters (and dialogues) in the game is quite difficult to find. Where something as simple as a maid that carries a weapon (a hidden weapon I only found because I knocked her out by mistake) can reveal more about a character than their entire dialogue tree.
Sure, it has it's flaws and it's not as impressive now as it was 15 years ago, but Deus Ex still holds up as an excellent game even today.
And while I have enjoyed a lot of games and some could even be considered to be better crafted (like Portal), none has had the influence or offered an overall experience that can hold a candle to Deus Ex.
Even Captcha can tell how much I love this game: Head over heels.