Just some more inspiration fodder for what you can bring to the start line:

*Mystical Creatures! Have them draw a chariot, ride them--heck BE one for all I care!
*Improbable Contraptions! Hamster balls of doom? Check! Want to convert your whole home into a race car? Done! Make it interesting!
*Broomsticks and Bedknobs! The classics never go out of style!

Really, sky's the limit. Literally. Racers can fly, swim, hover, hop or teleport to their heart's content. Fire harpoons at your competitors, take shortcuts, breath fire! Whatever gets you to the finish-line. Go full blown mad max or whacky racers.