I vote 'no' (in most circumstances). I'm pretty sure that most essay-writing books tell you to avoid it as well. Depending on the quote you use, it very well could be over-used in personal statements.
Generally you want to try and set yourself apart without hitting on too many cliches. (The little engine that could, Ghandi/Peter Singer Quotes, etc).
If you haven't done so already I would recommend picking up (or going to Barnes & Noble/Borders) and reading through the med-school essay books.. the ones with titles like 'essays that WILL get you into Med school.' Some of them actually have decent tips that I didn't think of when I wrote my PS. Because of the book I think I spent about 28 total hours writing up and revising my PS.
For the record, I did include a quote in one of the body paragraphs of my PS. It is a quote that I keep on my desk that has personal significance ... It's famous, yet fairly obscure quote that was written down and handed to me by my boss (and mentor) who passed away 5 years ago now. So it can be done... and I guess my take-home point is you have to be very prudent in how you use it, it's not necessarily a good 'attention grabber' like you would use a quote to open a standard essay for school.