I'm not even going to try to put these in order and if you asked me the same question on a different day I'll probably end up changing my mind on a few. I'll try and limit it to one game in a series too otherwise half of the list will be from the same series. Also while I'm basing these choices on the singleplayer components that's not to say that the multiplayer was bad for them, just that the singleplayer part is a more permanent and reliable experience.
Final Fantasy VI - I love all of the first 10 in the series, but this one's hard to top.
Sonic 3 & Knuckles - Doubles as the first game(games?) I ever finished. Unforgettable soundtrack. Nice level design with multiple routes to take and a much welcomed save feature.
Portal 2 - Great humour and atmosphere. Hints of backstory here and there in typical Valve fashion.
Devil May Cry 3 - The definition of kickass. Great soundtrack that fits the game and flashy combat that hits you harder than a glove full of concrete.
Fallout: New Vegas - Freedom, guns and a whole wide wasteland of people to trick, steal from and murder with dear old Mr. New Vegas accompanying it with the sweet sounds of the Mojave.
Dawn of War: Dark Crusade - W40K RTS perfection. Great music, especially the Guard's themes, visceral hand to hand combat and highly mod friendly.
Call of Duty (1) - Red Square. Need I say more? Again great music, particularly the Soviet theme and the main menu / credits. Blew me away at the time.
GTA: San Andreas - I liked Vice City's style and music more, but this was huge. Planes to jack, a jetpack and miles of free-roaming to do.
Warcraft 3 & TFT - Great story to these. A shame that the soundtrack isn't that of Warcraft 2 but the unit variety and item mechanics make up for it.
Tomb Raider 2 - Whilst I did prefer the Egyptian and Greek ruins of the first, fourth and fifth games I just have good memories of 2. It was when they'd gotten a bit more complex but hadn't yet become devious in their attempts to horribly murder Ms. Croft.