I received an e-mail request for my full manuscript this morning! My initial contact with this particular agent was because of a referral (she isn't accepting queries right now), but I pasted the first fifteen pages at the end of my note so that she could see if she liked the writing. And... she did!
She admitted that her reading pile is out of control and she might not even get to mine until summer(!), but she also said to let her know if I get an offer for representation in the meantime and she will then bump mine up immediately and see about "throwing her hat in the ring" as well.
Good stuff then.