I used to play Sonic & SEGA All-Stars Racing on my 360, I remember really liking this game, but from what I seen the newest one, Sonic Racing: CrossWorlds, is really good too, and it has Hatsune Miku which is super cool!

For games with no vroom vroom noises if speed is enough for you:

• I used to love playing Sonic Riders Zero Gravity, but from what I have seen online, the consensus is that the first Riders game is considered better, tho I never played it, and there's also a modding scene for both with competitive play. This video goes over it if you're interested.
• Haste is an indie game about running super fast that looks super cool, but I haven't played it yet.
• If you're into shooters, Ultrakill let's you get FAST, blasting through no stop at the speed of light scratches an itch in my brain I didn't knew could be scratched. Also the fanbase is thirsty for Gabriel (yes, the angel) and constantly makes yaoi of him and V1 (the playable character) if you're into that.

There's also arcade racers that tend to be beloved like Daytona for example, but I never played any of them.