Here are the 2001/2002 (or 2000/2001 in PS2's case) great releases on the other platforms, I left out all of the DC ports:
Gamecube
1. Super Smash Bros Melee (Fighter)
2. Luigi's Mansion (Action-Adventure)
3. Star Wars Rogue Squadron II: Rogue Leader (Space Shooter)
4. Pikmin (RTS)
5. Animal Crossing (Sim)
6. Wave Race: Blue Storm (Racing)
7. SSX Tricky (Sport)
8. Tony Hawk: Pro Skater 3 (Sport)
9. Eternal Darkness: Sanity's Requiem (Psychological Horror)
10. Metroid Prime (First Persona Action Adventure)
11. Resident Evil Zero (Survival Horror)
12. Star Fox Adventures (Action-Adventure)
13. Super Mario Sunshine (Platformer)
14. TIme Splitters 2 (FPS)
15. Baldur's Gate: Dark Alliance (Role-Playing Game)
PS2 (2000/2001)
1. Time Splitters (FPS)
2. Tekken Tag Tournament (Fighting)
3. SSX (Sport)
4. Onimusha (Action-Adventure)
5. Zone of the Enders (Action)
6. Red Faction (First Person Shooter)
7. Dark Cloud (Action-Adventure/Role-playing)
8. Twisted Metal: Black (Vehicle Combat)
9. Gran-Turismo 3 A-Spec (Racing Sim)
10. Klonoa 2 (Platformer)
11. Silent Hill 2 (Survival Horror)
12. Ico (Acton-Adventure)
13. Time Crisis 2 (Rail Shooter)
14. Okage: Shadow King (Role Playing Game)
15. Devil May Cry (Action Hack N Slash)
16. Grand Theft Auto III (Sandbox)
17. SSX Tricky (Sport)
18. Metal Gear Solid 2 (Stealth Action)
19. Baldur's Gate Dark Alliance (Role Playing Game)
20. Jack & Daxter: The Precursor Legacy (Platformer)
21. Shadow Hearts (Role Playing Game)
22. Final Fantasy X (Role Playing Game)
Xbox
1. Dead or Alive 3 (Fighting)
2. Halo: Combat Evolved (First Person Shooter)
3. Oddworld: Munch's Oddysee (Platformer)
4. Project Gotham Racing (Racing)
5. SSX Tricky (Sport)
6. Silent Hill 2 (Survival Horror)
7. Tony Hawk's Pro Skater 3 (Sport)
8. Elder's Scrolls III Morrowind (Role Playing Game)
9. Hitman 2 (First Person Shooter)
10. Timesplitters 2 (First Person Shooter)
11. Baldur's Gate: Dark Alliance (Role Playing Game)
12. Metal Gear Solid 2 (Stealth Action)
13. Tom Clancy's Splinter Cell (First Person Shooter)
14. 007 Nightfire (First Person Shooter)
15. Fatal Frame (Survival Horror)
