Because polyvinyl alcohol can be (ionically) crosslinked with borate to gel, forming a much less water-soluble polymer (though still a thermoplastic), I think you could do a useful 3-D printing system by extruding a solution of polyvinyl alcohol in water, either spraying the surface with a solution of borax or boric acid in between layers to solidify it, or submerging it into a tank of the same.
The polymer is already widely available, sold as a mold release, for about US$50/kg, and is biodegradable and non-toxic. (Borate is also pretty nontoxic, but it’s not in the same league as PVA.) It’s quite strong and stiff, comparable to PLA.
This system would have the following potential advantages over the now-conventional PLA FDM process developed by the RepRap project:
Alternatively, you could use it for a liquid-vat-hardening process similar to SLA, in which the liquid is selectively hardened not by selective exposure to light but by selective deposition of borate on the surface of a vat of liquid, using one or many nozzles, alternating with raising the level of liquid in the vat slightly. With the right crosslinking initiators, you could probably induce PVA to crosslink with light, too, which would probably form a covalently linked thermoset rather than the ionically crosslinked thermoplastic formed by the PVA/borate system.
There exist alternative crosslinkers for PVA that produce higher strength without UV, such as glutaraldehyde, which creates a covalently crosslinked material.