What DIY printers are there?

I keep hearing about RepRaps. Are they the only DIY 3D printers out there? Could someone list all the different RepRaps (main ones) and then list other DIY printers?

RepRap isn't so much a kind of printer as it is a community of people who design their own DIY 3D printers. There are quite a variety of vastly different designs that fall under the name "RepRap" and they tend to hold contests for the next "official" RepRap form factor.

Currently, the style that most people simply call a "RepRap" is the Prusia and the Mendel (something like 50% of the 3D printer kits you'll find follow the form factor of one of these two), but the Delta is also a well known printer format from the community. If you're looking for something a little diffeent, there's also the Simpson and the Morgan, both designed to have a minimum amount of precision parts, and therefore theoretically be the least expensive to make.

I'm personally a huge fan of the Simpson, which has no linear rails and a very compact, form factor... Sadly, it's still a work in progress and nobody seems to be selling kits for it.

Printrbot's are a good DIY printer, if you consider assembling a printer DIY. Most probably don't though.