Great idea, Kim...
Make sure you save an e-copy-either as a Word document/PDF/JPG so that you always have one and can print more as needed.
I'm not sure what field you're entering into, but it's always nice to have these letters match/coordinate with your resume-or stand out on the prof.'s own letter head too. Just think about that when asking for them/printing them. I went into the art/design/marketing field, so I always had things printed on funky paper with cool fonts so that my stuff had a better chance to catch the interviewers' eye.
The fact that you're posting this makes me think you're organized enough to keep them yourself
Don't waste $ on a letter service right now-JMO.
Best of luck to you!