I thought I'd come up with one of the cheapest most basic showers ever (just pouring water from a can is cheating) but I've been one-upped by this fellow:
Bunch of people at exp portal have used them; basically it's a nozzle for the ubiquitous soda bottles. Since I already make carbonated water in them (with tire valves, a bike CO2 filler, and cartridges from my BB gun) now I can use them for showers as well. Even less stuff to carry about.
Only gravity fed, but that'll work. I tried using liquid soap in my garden sprayer set up (one fillup with soap, another with rinse) but it got too sudsy. Might work with this, however. I've even got black plastic pipe I can put it in to heat up (or maybe black duct tape on one side).