Personally, I'm a fan of Biker Mice from Mars, RC Pro Am II, and Wipeout. Also, I have heard good things about Midnight Club II and NFS Carbon. 

Wipeout series by a mile for me!

Other ones I've always loved are F-Zero: GX, Tokyo Xtreme Racer (Dreamcast), Daytona USA, Sega Rally Championship, Looney Tunes Space Race, Crash Team Racing, Star Wars Episode I Racer, Project Gotham Racing 2, Colin McRae Rally 2.0, and Hydro Thunder.

If kart racers count I'll have to go with Diddy Kong Racing. I thought it was a better game than Mario Kart 64. After those 2 games I'd with Star Wars Episode I Racer.

I own the bolded ones, plus Tokyo Extreme Racer 2 but haven't had time to play them yet. ColinMcRae is a Rally game right? I plan on getting Sega Rally eventually. What's PGR2 all about? 

Yes, Colin McRae is a rally series. Overall, the franchise is one of the most consistently well-received racing franchises. The franchise's name was changed to "Dirt" after the real Colin McRae tragically passed away in the late 2000s. Still some great racing games. I primarily played the games that were released during the 5th and 6th generation consoles.

Gotham Racing was with Xbox starting with the original console's launch in 2001. Gotham Racing was the successor series to Metropolis Street Racer on the Dreamcast. They don't actually have anything to do with Batman or Superman lol.

But it's an arcade-style franchise that had interesting and fun mechanics to it. There was the "Kudos" system, where you could get points from combos by doing drifts, overtakes, not crashing, etc. So the game actively encouraged you to not only be like Tokyo Drift, but get better at racing. You also raced in streets from real cities around the world. Which was really cool to see, especially at the time. They found a really good mix of simulation and arcade racing. They never felt too much in either direction, so while you were wanting to be as good as possible, the games were still fun to play. There was also an arcade cabinet in your garage with this little side game called Geometry Wars which ended up becoming its own little phenomenon.

Oh and the soundtracks.......SO GOOD!!!!

First 2 games released on the OG Xbox, then 3 and 4 released on the 360. The series has been dead since. But it was one of Xbox's big exclusive franchises for a good while. Both the OG Xbox and the 360 launched with a Project Gotham Racing game to showcase their power.

F-Zero X takes the top spot for me for its crazy sense of speed and epic rock 'n' roll attitude.

Shoutouts to Diddy Kong Racing and Wipeout for also being excellent.