I'm not that much of a sports games fan (especially American ones I know little about) but the Sega games are just brilliant. Visual Concepts and Hitmaker did a wonderful job on these games.
Tennis, Football, Hockey, Basketball 2k2 series. Virtua Tennis 2k2 in particular. It's even better than the first game, if thats possible.
Fighter wise there's alot to keep you going. Keep away from VF3tb though. It's a bad port. Better to go for VF4: Evo on the PS2 if you want the best 3d fighter around. The neo geo ones are already in MAME, provided you have a pretty fast machine.
Street Fighter 3: Third Strike, Soul Calibur, Powerstone 1/2, Garou: Mark of Wolves, Last Blade 2, King of the Fighters DM: 1999, Fire Pro D Wrestling (the only good wrestling game I've played in years).
Some people find the sensitivity on Daytona a bit tricky, but its perfect with a wheel. Quite alot faster than the arcade original too.
Daytona USA: 2001, F355 Challenge, Crazy Taxi 1/2, le Mans 24hr, MSR.
And finally you've got some really, really good shooters. I play these games all the time. Bangai-O from Treasure is magnificent; like Robotron on steroids. The storyline is also hilarious.
Ikaruga, Mars Matrix, Gunbird 2, Bangai-O, Border Down, Zero Gunner 2, Cosmic Smash, Rez.
As far as puzzle/thinking games go I'd opt for the DC iterations of Puyo Puyo, Mr. Driller and Columns are all really coo.
You can't go wrong with any of the Naomi ports. They're still being released today. All the more reason to chip your machine and get them from Japan on import.