walmarts online store for $100 so I decided to give it a shot (they have since gone up to about $180). It was a bit of a revelation... apparently in the year I had gone without hot water I developed a whole new appreciation for the stuff.
All was well for a few months until the heater froze and started leaking. It turns out that there is a little cast-iron part that cracked. I tried fixing it with solder and jb-weld, but could not ever get it to work right again. At this point I had gone all soft and was addicted to hot water. I bought another one along with valves so that I could drain it when I was done (to prevent freezing). The second one worked for about six months, but I don't think they are meant to be used outside long-term... it started acting funny, shutting off randomly, it kept getting worse until it would not stay on for more than 10 seconds or so which made for a unpleasant, but probably very comical shower. Got a third one which somehow started leaking after a few months, even though it was drained completely after each use. At this point I was getting tired of buying these things and decided to try to make my own out of more durable and repairable materials.
It turns out that "making my own" was not nearly as simple as I had assumed. It took multiple tries and modifications to get it working adequately, so if you are planning on trying it please read on to see all the things I screwed up.
For version three I added another 20 ft of tubing in a coil around the first one and then added another valve between the heater and the shower head. This one determines the flow rate and prevents vapor lock, while the one by the garden hose determines on/off. The result was much better... pretty much equivalent to the store bought version. I thought that I could get it even better by increasing the surface area again. So I got a bunch of stainless steel scrubbing pads at the dollar general and pushed them between the coils. This basically acts like the fins on a radiator and conducts more of the heat from the flame into the copper tubes. More copper tubing would have done the same, but this was less expensive.
The cost was about $50 for the propane burner, $60 for the copper, $10 for the two valves, and about $20 for various other materials, joints, solder, etc. So at $140 I am not saving much, but I expect this one will last a lot longer and is easier to repair if something does happen. It is still likely to freeze this next winter so I need to figure out how to fix that before then.
It is definitely not as automatic as the store-bought one, you have to turn the water on first, then the propane, light, shower, then turn the propane off and finally the water. Screwing this up will probably break something... the solder will melt if there is no water flow, and the water will turn to steam, build up pressure and rupture something if it goes on too long.
If I were doing it again, I would probably try to buy a 50ft coil of copper, and would use a metal bucket instead of a clay pot. Basically the larger the coil the more surface area you have and the hotter the water becomes. Let me know if you figure out any other tricks to improve or simplify what I have above.