The Mario Kart games usually take place after the last canon Mario game..
Super Mario Kart had locations and characters based off of everything up to Super Mario World.
Mario Kart 64 had everything up to Super Mario 64 (I think that was the last one released before MK64..)
Mario Kart Super Circuit had.. well, it was a revisitation to what made SMK great, while throwing in ideas that were in the second game (and a few ideas of its own).
Mario Kart Double Dash had everything up to Super Mario Sunshine (and two riders per kart. Whee!)
Mario Kart DS had everything up to.. it, too was a remix of all things Kart, while introducing new ideas.
I haven't played Mario Kart Arcade, but I usually consider the MK games to be somewhat canon, since they show locations of things (ie: in MK64, Mushroom Castle proximity to the Royal Raceway..)