One way I have figured out to do this is to be someone fairly light weight (e.g. Toad or Yoshi), then get a buddy to play as a heavy-weight (e.g. Donkey Kong). Next, have them line up right near the wall, facing towards it. Now you will need a mushroom and to line up behind them. Once you are lined up, you stand a little behind them such that the mushroom will give you enough power to run into them, normally causing your character to spin out. Right as you hit them, though, press the R button to jump. If timed correctly, this will launch you fairly high up, enough to jump over most walls.
If you time it correctly, you might even be able to do this without organizing with a buddy, since this does work while the heavy-weight is driving. It just might be really hard to line up correctly while both of you are driving.