Sonic Adventure 2

Kart racing mini-game (Hero side)
Finish Tails' driving quest in the Hero side story

Kart racing mini-game (Dark side)
Finish Rouge's chase mission in the Dark side story

Boss attack mode
Finish the Hero or Dark side story modes

Last stage
Finish the Hero and Dark side story modes. After, go to story
mode and a "Last Stage?" option should be appear in the menu

Unlock Super Sonic and Hyper Shadow
Finish the "Last Stage?" in story mode

Unlock 3D version of the Green Hills Zone, from Sonic The Hedgehog:
Collect all 180 emblems (including Kart, Timed Boss) for all "A" rating.
This will unlock hidden multi-player characters also.

Unlock characters in alternate costuems in kart moe:

Unlock Amy Rose
Finish all of Sonic's levels and missions with an "A" rating

Unlock Metal Sonic
Finish all of Shadow's levels and missions with an "A" rating

Unlock Tikal The Echinda
Finish all of Knuckles' levels and missions with an "A" rating

Unlock Sonic in PSO suit
Finish all of Sonic's levels and missions

Unlock Shadow in alternate costume
Finish all of Shadow's levels and missions

Unlock Tails in the Tornado 1
Finish all of Tails' levels and missions

Unlock Eggman in alternate Eggwalker
Finish all of Eggman's levels and missions

Unlock Knuckles in alternate form
Finish all of Knuckles' levels and missions

Unlock Rouge in alternate costume
Finish all of Rouge's levels and missions

Full pause screen -
Press X + Y, while paused the gameplay.

Secret images:
If you insert your game disc into a PC CD-ROM drive, you will find
lots of images from the game.