I find these types of lists quite valuable. If anything defines a console, it's exclusives. Just to help clarify things...

Army Men Air Combat: The Elite Missions is an updated release of the N64 title.
Backyard Football was released on PS2
Bloody Roar: Primal Fury was released on the Xbox as Bloody Roar Extreme.
Evolution Worlds is a re-release of the Dreamcast games Evolution: The World of Sacred Device and Evolution 2: Far Off Promise.
Metal Gear Solid: The Twin Snakes is a remake of PlayStation Metal Gear Solid.
Summoner: A Goddess Reborn was released on PS2 as Summoner 2.
"The GameCube port was released as Summoner: A Goddess Reborn in 2003. The characters of Maia and Taurgis are redesigned from the original (the changes to Maia can be seen by looking at the box art), and there are slight visual differences in some levels (most notably the Palace of Halassar). The GameCube version unfortunately has a significant frame rate stutter during combat, which was not in the PS2 version. It also lacks a hidden cut scene referencing the first game. The gameplay, features, and story are identical." -wikipedia


Bomberman Jetters was released on PS2 in Japan
Chaos Field was released on Dreamcast and PS2 in Japan and on Wii as part of Ultimate Shooting Collection
Ikaruga was released on Dreamcast in Japan
Space Raiders was released on PS2 in Japan
Spirits & Spells was released on PS2 in Japan and Europe
Tales of Symphonia was released on PS2 in Japan
Tom Clancy's The Sum Of All Fears was released PS2 in Europe
Worms Blast was released on PS2 in Europe


Because it's so easy to play Japanese imports on the Gamecube, an updated list including Japanese exclusives would be even more valuable.