Red Dead Redemption - Horseshoe throwing
GTA IV - Bowling, Pool, could the whole relationship thing count as a mini-game?
Final Fantasy VII - There were some awful mini-games in the golden saucer
Final Fantasy IX - The card minigame fails to capture the simplicity and elegance of the card game in FF VIII
Final Fantasy X - Blitzball has been mentioned already in this thread
Final Fantasy XII - I could never grasp the quickening system, seemed completely random
Super Mario Galaxy 1 & 2 - Clearing out the trash (1 is slightly worse)
Shenmue - was it called Lucky Ball, the pachkino game
I haven't got far enough in Mass Effect yet to start exploring the planets (just became captain of the Normandy so I'm sure I'm near it soon) so I guess I have that to look forward to.