DH and I are both grad students with fellowships/assistantships, and he has a part-time job outside of school as well. I think all of this puts us in the lower-middle class category.
We put about 25-30% of our take-home into savings each month, and even that never seems like enough. Our goals are all still so far away! We're young (25), so we have a lot of savings accounts and goals, though: a too-small emergency fund we're building up, a down-payment fund, saving for a baby, an IRA (we don't have 401k's in grad school, of course), a travel fund, plus we have savings accounts for semiannual insurance bills (so if you count those as bills instead of savings, we save more like 20-25%).
I'm by no means an expert, but I'd say 10% is probably on the low side.