Not classic yet, but out-dated.

[BumblebeeCody]

The Legend of Zelda Wind Waker
Super Mario Sunshine
Resident Evil 4
Animal Crossing
Donkey Kong Jungle Beat
Super Smash Bros Melee
Sonic Adventure 2 Battle
Mashed
Tales of Symphonia
Call of Cthulu: Dark Corners
Marvel vs Capcom 2
Timesplitters: Future Perfect
Viewtiful Joe
Chibi Robo
Street Fighter 20th Anniversary
Killer 7
God hand
Munches Oddysee
Okami
^^^^^
I think those games are great classics that can hold out pretty well even today. There are some games like Billy Hatcher and Baiten Kaitos which are great but may not have the appeal anymore.

Others:
All of those HD Collections (MGS, DMC, GoW, SH etc) <- prove those games still hold out today.
Shenmue??? <- It really depends on the player to see if stands the test of time

I find that games of the fun sports/fun racing/sim and fighting genre survive the best because it's not about the graphics but the mechanics of the game. Mario Tennis, Mario Kart, SF3: 3S/MvC2, Populous for example...

Some genres evolve over time. Look at how the FPS genre evolved
Wolfenstein > Doom/ > Goldeneye/Quake(PC FPS)> Timesplitters/Metroid > CoD
Notable differences such as, Health pickups being replaced by (irritating) screen turning red. No weapon pick ups. Multiplayer game modes. But a game series like Zelda doesn't need to evolve.