Ill assume for the moment you will be buying original copies so rare games will not be mentioned.
First you HAVE to own Shenmue. No Sega fan will take you seriously if you don't
Quake 3 arena can be played over the network
DOA2 is a must have fighter followed by Marvel vs. Capcom 2
Jet grind radio is a rollerblading graphiti game that everyone will like
MDK2 is a great single player FPS
Chu Chu rocket and Bust a move are the best puzzles
Mars Matrix and Gunbird 2 are perfect scrolling shooters
Edit: How could I forget Bangai-o (crazy robot action), Space Channel 5 (like Parrapa), Bomberman online, Resident Evil Code Veronica (the best version available) and of course Crazy Taxi (very true to the arcade)
Will you consider playing copied games? No modchip is needed...
If so here is a list worth looking at
http://www.racketboy.com/retro/2006/...st-import.html