Unreal Tournament - This game was amazing for it's time, incredibly fun multiplayer based gameplay with fast-paced arcade elements to it. Unreal Tournamet 2003/2004 were good but just not as impressive as the original game. Unreal Tournament 3 was decent I guess but just a dissapointment overall.
Warcraft 3 - I spent all night playing this game after I got it, it's just an incredible, amazing game, the campaign is really really good and the multiplayer is superb, there's just not much else to say about this, I have really fond memories of playing this game.
The Sims - I was blown away when I first discovered my brother playing The Sims, it was such a novel concept and it was just so incredibly fun to design your sim, manage his life, improve your house and discover new things. The first expansion (Livin' something) added a lot of wacky stuff which I loved.
Doom 3 - I have never ever been as impressed with graphics as I was when I first played Doom 3, the graphics were just a MAJOR revolution (along with Far Cry and Half Life 2 but I played Doom 3 first out of those three), I don't think there has been a change as drastic since then. I was so completely immersed and I liked the gameplay too. Crysis came close to blowing me in the same way Doom 3 did, but not quite.
Heroes of Newerth - I got in the closed beta way back in 2009 and I haven't looked back ever since, I still play this game today and it's amazing, it's really fun, I've met a lot of cool people and had a great time playing it. I've played this game probably more than any other game in my lifetime.