As far as i remember, Diddy Kong Racing was the first racing game i played. I still remember its first boss.
Then comes the subgenre i like the most, the discovery of futuristic racing games with Extreme G3. While the action aspect isn't something i'm looking for, what i do love here is the mix of both high speed and unconventional tracks. Did you really experience a racing game if you never turned your head and your controller to go along the vehicle you're controlling?
I continued digging the genre and i remember Killer Loop there. Not a lot of content, but enough to enjoy it back then.
Speaking of content, Redout is the opposite in that matter, with up to 60 circuits. With an interesting take on the controls, having (for the default scheme) to use both sticks: one to turn, one to strafe. I liked most of it, except for the need to wallbounce. They're often faster than clean driving, sadly.
I still enjoy some less crazy racing, if we may say so, like the Trials or the TrackMania series. Easy to learn, hard to master. Community driven with a powerful track editor. Some unexplored possibilities too in TrackMania as you can integrate code (ManiaScript) in your maps. I improved an already existing tool and put it on GitHub to track players progress in quests you may want to put in your maps.
What impress me though, are the TrackMania RPG mappers. Hard to choose one to highlight, but here's Location of Ascension by Skyslide. Shortly after i discovered this style, i opened several servers for their maps, still up.
1: With the permission to do so by the beneficiaries.
Note: The listed games are those which spontaneously come to mind. The purpose is to give you an insight of what i like the most in this genre.
Credits: XGIII: Extreme G Racing (Extreme-G 3) by Acclaim Studios Cheltenham, Diddy Kong Racing by Rare.