For random map mode:
The Age of Empires series
Rise of Nations
Age of Mythology
(forgot Stronghold Crusader)

For multiplayer:
Super Smash Bros. series
Mario Kart

For a platforming binge:
Yoshi's Island (GBA)
Mario Sunshine
Super Mario Brothers 3 (GBA)

Reliving Gamecube days:
The Legend of Zelda: The Wind Waker
Animal Crossing

When I want to shoot something:
Battlefield 2
Delta Force: Black Hawk Down

For the "Grand Campaign":
Rome: Total War
Medieval II Total War

I return to Skyrim quite often, Oblivion also.
S.T.A.L.K.E.R. series, but usuall Call of Pripyat.
Amnesia: The Dark Descent & the Penumbra games.
Terraria.
Quake (the first one plus mods at times)
Universe (Amiga game)
Guild Wars.
Giana Sisters.
Don`t Starve.
Killing Floor.

Yep, it's amazing how much progress they've made on that.

Devil May Cry 3 SE
Gothic (1-3)
Heroes of Might and Magic (2, 3, 5)
Neverwinter Nights (1/2)
Praetorians
S.T.A.L.K.E.R. (CoP/SoC, vanilla and modded)
Stronghold (original/Crusader)
The Elder Scrolls (3, 5)

The Witcher 1, 2

Neverwinter Nights 1, 2
Oblivion
Skyrim
Fallout 3
Fallout New Vegas
Borderlands

Mass Effect 1, 2, 3
Dragon Age Origins
Dragon Age 2

I've beaten Resident Evil 4 about 10 times, so I have obviously gone back to that a ton. I also go back to Ghost Recon Future Soldier quite a bit (the campaign is amazing).

PC:

Gothic 1+2
GTA San Andreas

SNES:

King of Dragons
Secret of Mana
Final Fight 3

Atari 2600:

Phoenix
Crystal Castles
Solaris
Jungle Hunt
Defender

PES6 on PS2, no doubt the best football game ever.
Also at some occasions we (me and my brother) play Fifa 11 on 360. Haven't been bothered to get newer one, this is still as good.

Tropico series (especially the first one) and also Children of Nile are games I keep on replaying every few years.

Cyberia.

And no, not Syberia, Xatrix's Cyberia (the same people who made Redneck Rampage and Kingpin, which are available on GOG), but they do both share the setting, kinda.

It's a weird mix of a cyberpunk adventure game AND an arcade-y rail shooter. And, to tell you the truth, it's terrible - it relies on trial and error-based game design, having the player to die a thousand times before memorizing what to do in each section in order to beat it, including both adventure and rail-shooting aspects.

It is unintentionally hilarious, though. Not talking about the pre-rendered 3D graphics which didn't age well at all, I always thought the main character is butt naked (..could you blame me? He's wearing a skin-tight, skin-colored latex suit!! ..and he goes to freakin' SIBERIA wearing that!)

The worst part is that I have no clue why I replay this game every year. Maybe because of nostalgia since this was the first game I've ever played in my life..? (It came bundled with a new magic box that was called "cowmpewtoor", back when I was a little kid)

You can take a look at the game in Game Informer's hilarious super-replay of it. And yes, it has an equally terrible sequel.

The arcades released after the golden age and the big video game crash of the Eighties (Ghosts'n Goblins, Ghouls'n Ghosts, Raimais, Rolling Thunder, Black Tiger, Green Beret, Commando, Section Z, Exed Exes, The King of Fighters '97 etc. etc.).

Diablo II on the PC. Another World, Flashback, Eye of the Beholder, Speedball II under DOS.

On PC:
Master of Orion 2
Star Control 2 (or Ur-Quan Masters - I alternate them)
Civilization
UFO: Enemy Unknown
Diablo 2
Arcanum

On consoles:
Mass Effect series
Dragon Age
Kingdoms of Amalur

On PC
Quake - no other game captures the same fast paced action.
Max Payne 2 - it never gets old shoot dodging in bullet time and watching npcs drop like ragdolls.
Far Cry - It's so pretty and scratches a very specific itch I have.
Trine - relaxing yet challenging and absolutely beautiful.


On ps3
Uncharted games - 'cause they're good, that's why
Dead Nation - best zombie shooter. Great upgrades and intense challenging action

On xbox
Timeshift - great action combined with time manipulation
Mirror's Edge - completely unique game with a great challenge and atheistic
Shadow Complex - It's Metroidvania at it's best
Mass Effect - duh

Deus Ex. Do I have to explain this one? It's just a great game. Really.

Knights of the Old Republic I and II. I've played these two games many times and I still experience things a little differently each time I play.

Mass Effect series. In the three years I've owned the first two games, I've played them six times. I've played the third one four times in two years. Why? Because they are fun and unique experiences that are different each time I play them. They're great.