Well, actually, I didnt tell them how many at the outset. And I apologized profusely throughout. But more than that, Ive done research with two of them, and the other is the advisor to an association Im in charge of, so it is not the sort of situation where I just took thier class and got an A. I also showed them the admission statistics, to show the legitimacy in applying to so many places.
Rsaylors is right about how its relatively easy-there is typically just one letter they use for all of them, unless they are an alumni. Ask nicely and ask early though. And always be unendingly polite, even if your recommender likes to submit each one of them the day before they are due, grouses, or needs a spreadsheet with deadlines and links.
One thing I noticed, that I thought was pretty neat, was that I kind of felt they all wanted to do it. I mean, if they see some kid who is quiet, smart, and going on the same path as they did, I think they feel a sense of duty to help him/her out.