How about a generic game just about everyone owns and can be played on the console rather than emulated. For high scores a picture should be taken of the TV/monitor (for those using RGB/VGA/DVI) for legitimacy. Also if there's a difficulty setting for the game, maybe different levels could be distributed to seperate experts from newbies.

Some suggestions:
R-Type
Darius
Super Mario Kart
Tetris
PuyoPuyo

Ideas on how you're ranked:
Side-scrollers: Points and difficulty
Puzzles: Level reached and points
Racing: Lap times