I can tell I'm touring in the wrong part of the world... After reading all these comments about being able to actually SHOWER in CAMPGROUNDS, well.... let's just say I would be thrilled to actually find a campground. (I have been told there are tons of them here in Argentina, so I'm hoping we actually find some of them - we've only been in this country for 400 km so far)
Basically, I ditto what's been written above - shower is great if one is available. After that, I would happily settle for a jump in a lake or river. Trouble is, we don't find many rivers or lakes in the Peruvian desert or Bolivian altiplano... And the restaurants only have a small basin of water sitting out front to wash your hands in. Running water is a major luxury.
What I mostly do is use some water from my water bottle to wet a washcloth and wash up with that. Obviously I can only do that if I have enough water to spare, which I frequently don't. For those times when I don't, I carry around wet wipes and use them. I really don't like all the lotions and junk they have in them though - Wet Ones are the best I've found, so I carry another local brand for washing hands after changing tires and such and reserve the Wet Ones for washing up in the wild.
We also found we almost stayed in hotels throughout Colombia, Ecuador, Peru, and Bolivia just so that we could wash up. It was well worth the cost of hte hotel in order to be clean.