Sonic Pinball Party is a video game released for Game Boy Advance in 2003. It is a celebration of sorts for Sonic Team featuring many references to its previous games, mostly Sonic.
The story is set in Casinopolis (in Station Square), where Doctor Eggman turns the people gambling into robots, and brainwashes Miles "Tails" Prower and Amy Rose. Sonic must rescue his friends by winning a pinball tournament called the "Egg Cup Tournament."
The game features three Pinball tables, based respectively on Sonic Advance, the Sega Saturn classic Nights into Dreams..., and the Dreamcast/arcade game Samba de Amigo.
The player must defeat Eggman to move to the next area in the Sonic board. The player moves to the next area when they collect all the Ideya and defeat the Nightmaren in the NiGHTS board. The Samba De Amigo Board never changes, as there are no real objectives except for getting a high score.
In the Sonic board, shooting the ball into a hidden hole three times changes the character shown on the table from Sonic, through Tails, Knuckles, Amy and back to Sonic.
Source: Wikipedia, "Sonic Pinball Party", available under the CC-BY-SA License.