It started one night when I was beginning to tell one guy who approached me, "No I don't have any--" he interrupts and says, "Naw man I just want some food." I make more money than I need, so we go to a nearby Chinese place (his idea) where they seemed to know him. They wanted him to wait outside, but I sat out there and listened to him ramble while he waited for his meal. He talked about how his girl had been pestering him to marry her for 17 years, and how people will betray you and such.
I was late to meet my friends for dinner, but the experience had an effect on me and helped reset my worldview a bit.
In Amsterdam, I'm cautious, especially if I'm traveling alone. I'm female, and though I know security is there, some people are pretty agressive anyway. I've given a cigarette here and there, but nothing more.
When I lived in the states, it would depend on the situation. I assumed most folks were lying, but would give change or a dollar or two occasionally, depending on attitude. I've occasionally bought a cheap meal for folks, or coffee.
I figure overall, a few folks really needed the money or were really appreciative, so it all works out. I'm not giving anything that takes food or anything away from myself, so I'm not losing anything either. I wish no one needed to do such things, or lie about their situation or be able to earn more begging than with a normal job - but that's not the world I live in right now.