If you rent and your landlord tells you not to put holes in your walls, suction cup hooks are a good solution for the bathroom. (Just don't try to shave your legs in the sink.) More below.
Although they won't hold heavy things like towels or robes, suction cup hooks adhere well to tile and will hold small objects. You can also use them on a mirrored surface, or inside the medicine cabinet. For a little extra staying power, try power lock hooks, or for a suction-cup alternative try Umbra's Cling Hooks ($4.50 each).
Image via Orla Kiely Spring/Summer '03