Samba de Amigo Table - Defeat Knuckles in Story Mode.
Slots Mini-Game - Defeat Tails in Story Mode.
Bingo Mini-Game - Defeat Amy in Story Mode.
At the character select screen, Highlight Sonic and press Up, Tails and press Down, Knuckles and press L, Amy and press R, then select Sonic. Tails will help Sonic and follow him around, just like in Sonic the Hedgehog 2.