Favourite Kart Racer overall has to be Mario Kart 8. I love and have a ton of nostalgia for Mario Kart 64 with its battle mode, but if you wanna play with friends the modern conveniences like HD graphics are nice. Honorable mention goes to Snowboard Kids. Takes the kart racer formula and puts it on a snowboard. Tons of cool ideas that sadly never made it to modern consoles.
Favourite Arcade Racer: Need for Speed Underground. It oozes style, the OST is great and it ramps up its challenge nicely. By the end you really gotta know your turns to get through.
I don't really play straight up simulations, so I can't really comment on those, sadly.