The reason I put this as arcade/puzzle, is that you sometimes (like level32) have to puzzle what way to take. This means that if the obvious path is to go right, you sometimes actually have to jump left on the wall and take an easier path.
Also, if you hold the jump button, you can jump quite far. Somtimes over 2 obstacles at once.
Did I mention you can jump diagonally, as in, jump and hold left/right to jump in that direction, which works on walls too.
EDIT:
I just replayed level 32 again. It was very easy. Got past on the 2nd try. This one is all about knowing when to go to another wall.
So I thought, lets record you a movie getting past.
spoiler video:
http://files.lpchip.com/temp/flashmovies/Run2Run/r2r_l32.htm