I've seen an interesting method to deal with these people. Give them 10gp to see if they are grateful, then decide if you want to give them some more. Although, I personally don't hand out to beggars.
I think just 10 GP would be a petty amount and sort of a slap in the face to some :(. I'd rather start off with 1,000 GP. I can imagine people becoming very good friends over that though!
