Like Dana, I give what I can, when I can.
It's rare that the change in my pocket will mean more to me than it does to them - when it does, I look them in the eye and say, "Sorry, I have nothing."
I buy the Big Issue weekly - magazine that (registered) homeless sellers buy for 70p and sell for £1.50. I have a regular seller that I buy from, outside the Co-op. If I've bought it from someone else and have money in my pocket I will ask him if he wants anything from the shop. This varies from a banana, to a non-meat sandwich (I think he's Muslim - middle Eastern in appearance and accent) or a can of Red Bull (!). He recognises me, notices my hair changes and always says, "God bless you, God bless you!" Well, I don't mind that too much
I was brought up on the Gospel of St Matthew. Even my hard-bitten East End Nan used to give money to people on the street. Not beggars, but pavement artists, buskers, the performers in Covent Garden. Her credo was always - if they're that down on their luck they need it more than I do (she was a very proper lady and would have died rather than performed in public).
Also, we used to have charity collecters in town every Saturday. Our big thrill was to get 2p from Mum and run over to put the money in their collection tin. We'd get a big smile and a thank you and a sticker. I know "beggars" are not the same thing, but childhood experiences all count in this type of scenario.
PS - Bruce? I lol'd.