Avoid Giving Handouts
Once you see how big of a gap their is between your own standard of living and the rest of the world, you'll be more than tempted to start doling out your dollars worldwide. Don't forget, however, that the most constructive role tourism can play in a depressed economy is not random handouts but to encourage legitimate and sustainable local business.
Considering that a high proportion of money earned by package tours stays in the hands of foreign investors, independent (all be it budget) travelers have a particularly high level of control over where their money goes. Collectively backpackers, even just the visitors to this site, can make a difference by not salving their consciences with a few ultimately meaningless donations to beggars or children, but by thinking about how and where they spend their money and whenever possible lending their support to locally owned businesses and community projects.
Gifts For Children
You should have very little time or love for those travelers who carry around sweets or trinkets which they then hand out indiscriminately to children. The motivation for this sort of thing is entirely selfish, in that it makes the giver feel good about him or herself while giving these kids even more dental problems.
Don't encourage children to beg, for their own sake and for other travelers. There are towns and villages all over the world where even right now children will ask travelers for money or sweets ('bon-bon' is a favorite) or a pen (another favorite implying education - the child is just smarter than the one asking for a rupee or a dollar) perhaps a hundred times and hour.
Oftentimes, children who are successful beggars will be kept out of school to continue working the streets or they are forced to relinquish their earnings to gang leaders (a la Slumdog Millionaire). Of course there are other places where children are genuinely friendly and never ask you for a thing and all it will take is only one naïve tourist and a big bag of sweets to transform the latter into the former.