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Off the top of my head, any of these games I can pick up and enjoy them for hours on end like a little kid again:
HALO 1(obviously)
HALO 4
Paper Mario
Star Fox 64
Gex: Enter the Gecko
Spiderman 1 (N64/PS1 version)
Pokemon Red
Mario Kart 64
Super Smash Bros Melee
Brothers in Arms: Road to Hill 30 (that's where our Hill 30 gametype comes from)
Brothers in Arms: Earned in Blood
Red Dead Redemption
Elder Scrolls 4: Oblivion
Left 4 Dead
Animal Crossing (ALL OF THEM.)
Star Wars Republic Commando
Star Wars Battlefront 1 (2 was alright, but 1 had much better maps)
Assassin's Creed 2
Gauntlet Legends & Dark Legacy
007: Agent Under Fire
Super Mario World
Call of Duty: Finest Hour
Medal of Honor: Frontlines
Duke Nukem 3D
Pokemon Snap
Conker's Bad Fur Day
Yoshi's Story
Crash Bandicoot 2
Spyro the Dragon
Soul Calibur 2
Rampage: World Tour
Mario Party 2
Castlevania: Symphony of the Night
NHL series
Honorable Mentions:
Far Cry 3
Tomb Raider
Call of Duty 2 (NO NOT MW2 YOU IDIOTS. I'M TALKING ABOUT WHEN CALL OF DUTY WAS A MUCH MORE RESPECTABLE GAME SERIES AND EXISTED BEFORE 2007).
Bioshock
Chromehounds (Multiplayer only)
Battlefield 2: Modern Combat (Multiplayer only)
Halo 2 (Multiplayer only)
Portal 1 & 2
GRAW 2 (Multiplayer only)
Legend of Zelda sucks.
Shit, the more I think about this, the more games I realize i'm forgetting.
OG Xbox:
Mech Assault
Full Spectrum Warrior
Freedom Fighters
Xbox 360:
Condemned: Criminal Origins
Fary Cry 3
Assassin's Creed 3
And don't even get me started on N64, there's too many to count.
I think I forgot to mention Fallout in my original post so I am mentioning it now :)
Homefront
Halo Reach
Call of Duty 4
Fable: Lost Chapters
Halo CE
Final Fantasy 1 - 9
Halo 4
Assassins creed
Assassins creed 2
Cromehounds
Super smash bros.
Mirrors Edge
Star Wars Battlefront
Starwars knights of the old republic 1 and 2
Starwars republic commando
Starcraft
I totally forgot about Homefront and Mirror's Edge. Those two also.