I apprenticed at the Walnut Street Theatre in Philadelphia in the 2000-2001 season. It was an incredible experience. Once the shows opened (and they produce big-budget musicals and plays), it was me on stage left and the other apprentice on stage right--you work as a fully functioning ASM and I can't imagine a better way to learn.
As for the stipend, it was, at that time, $275.00 a week. No housing, but I was able to afford my own studio apartment in center city, a seven minute walk to the theatre. Money was tight, no doubt. But I was able to get by and still go out for a good time once in a while. They also provided health insurance, and if you can find the time, free classes in their theatre school. I also spent the summer after my apprenticeship as the production manager of their summer camp and went back the following two seasons to stage manage their non-equity "Christmas Carol" on the mainstage. I also can say that having those credits on my resume definitely helped to make my phone ring more often after working there.