It sounds like I'm being a bit harsh here but there is a really big problem with lots of locations around the world where beggars are not genuine, there is nothing wrong with the person in question and even stories of criminal gangs that force these people to beg and the beggars themselves don't actually get to keep the money.
The scene from Slumdog Millionaire comes to mind where they were actually burning out children's eyes in order to make them better earners on the streets. I have no idea if that actually happens, but it doesn't seem beyond the realm of possibility.
I remember I was traveling through Asia and I gave a tiny bit of money to a little girl who was selling flowers at night and my friend who i was visiting and who lived there told me that "you really shouldn't do that, those kids are intentionally kept out of school to make money for gangs."
He had lived there for a while so I kind of just assumed that he had some idea what he was talking about but then as I traveled more and more I noticed that this idea of pathetic little girl selling flowers was something that was taking place all over the country and at night, when that kid should probably be sleeping in order to go to school.
I have heard and have witnessed situations where the beggars were far more aggressive than this and it always seems to be in tourist locations. One sure fire way of knowing that the begging is not legit is to watch them as they leave. Do they approach locals or just travelers? From my experience they don't even bother with the locals and I don't know why this is but it certainly seems that way.
This doesn't mean that you shouldn't have a heart and if you are concerned about the people in this countries or areas there are almost certainly places and foundations that you can donate your money or your time to and these organizations are probably much better at getting help to the people that truly need it rather than to just people who very well could be part of a criminal enterprise.
There are some parts of the world that I have been that any sort of begging, busking, or even selling of items is forbidden and honestly, this makes for a much better journey anyway. There is nothing worse than being pestered around every turn to spend money and to be bombarded with sellers of things around all turns.
Plus, sometimes these beggars are able to make more money by begging than by having an actual job, which is an insult to the people who work hard to make a living. It also encourages more people to enter this trade and it gets flooded with people who are not genuine.
This is not just in the case of poor countries. I remember a time when there was a guy on the side of the road that had a sign that said "Will work for food" as this was all the rage. I stopped by and gave him some burgers from MCDonalds and he put them in his bag. When his bag was open I could see a ton of money, lots of other food, as well as other gifts. This guy wasn't hungry, there was nothing wrong with him, he was just looking for handouts rather than working.
There is another story where the small city I lived in had its first beggar and the community got together to organize a job and an apartment for him. They also gave him the first week's pay up front. When his first day of work was to begin he didn't turn up.... someone went to his apartment only to discover that he wasn't there. He didn't want help to make it in life, he wanted a handout. He moved to another city to do the whole thing over again.
When traveling, it might seem like "oh it's just a dollar, it doesn't matter" but when everyone thinks that way it makes the stuff in the image above come and continue to stay true. If you really want to help, volunteer your time or donate to a real charity. Unfortunately, giving to beggars is a bad idea when traveling.