Database for proteome-wide predictions of protein structures
There are three initiatives I know of to have a go at this:


PConsFam, which collects data from this paper.
The Baker group's metagenomic study which you mention in the question.
The recent DMPfold work from our lab. This compares its results to the above two studies and discusses the effect on various model organisms.


The second and third of these don't provide a database per se, but the models are available for download and are linked to the Pfam database.