If you do accept votes for any Mario Kart games, my vote goes to MKDS for the Missions mode, as it had some good ideas that were executed well for being just a fantasy racing game.
Hoo.. But I digress.. It's hard to say what Mario game really had the best races outside of the SMK series..
Luigison is right, SMBDX has a mode in which Mario races a ghost to the flagpole, so I guess that would work.
New SMB's two player mode has the Bros racing to collect Stars (as in Power Stars), so I like that one a lot.
Mario RPG has the race against Boshi..
Are we allowed to make multiple votes? I'm having a hard time picking just one again.. XD