If you count skateboarding, Tony Hawk’s Pro Skater 2 is easily the best sports game on PS1.
And if you count auto racing, the Gran Turismo series is usually acknowledged for being great by PS1 standards.
After that, it takes a pretty sharp drop and it’s a very subjective argument…
FIFA 99 is pretty good, and there are six more FIFA games that came after it that I’m sure are good too.
Early installments of the Pro Evolution Soccer series are well-regarded. I can’t vouch for them, but I hear that ISS Pro Evolution 2 (released in 2001) is very good.
The late Madden games, Madden NFL 2001 through 2005, are decent but very chunky looking.
NFL Blitz is simple fun, but you’ve probably played that on any number of other consoles.
Some people claim that NHL 99 through NHL 2001 are good, but I’d caution you on that. They’ve aged horribly.
I have a huge soft spot for NHL Open Ice: 2-on-2 Challenge and a tiny soft spot for the first NHL FaceOff game.
There’s also NBA Jam: Tournament Edition, which I hear doesn’t play nearly as well on PS1 as it did on the 16-bit consoles, and then there’s the followup NBA Hang Time, which I find underrated, but looks better on N64.
Baseball games, just forget it. I have yet to play a PS1 baseball game that I like.