When traveling, you will without a doubt come across people asking for money. After all, poor people everywhere will reason that anyone who can afford to travel – by definition – has money to spare. Even a "budget" traveler may be much richer than most local people in some places; according to UN statistics more than a billion people live on less than a euro a day.
Consider giving generously if you want to, but remember a few points.
- Give only when it is your choice. Don't give to obnoxious or intimidating beggars just to get rid of them; this may solve your immediate problem, but it encourages them to try the same tactics on other victims.
- Keep the amounts in proportion; in a country where many people work long hours for a few euros a day, giving a beggar a euro is wildly excessive. In China, for example, giving one yuan (about 15 cents) is generous; many Chinese would give half that and a beggar who collects 100 yuan a day is making considerably more than most factory or construction workers or most waitresses, even in "five-star" hotels.
- If you do give, be discreet. Otherwise, you may mark yourself as an easy target and attract all the other beggars to see what they can get out of you; this can quickly ruin your trip.
Some people who beg are doing so out of desperation. Most, however, are not desperate at all; begging is their chosen profession and they make very good money at it by local standards. The truly desperate will not be found begging in most cases. Instead beggars will have their schtick which they have honed over the years (or through adult training for the children) and will have key choke points marked out for themselves where they can make good money. A truly desperate person simply won't have the skills (or the taste for violence) necessary to compete in the begging marketplace that surround the tourist hot-spots and begging out in the bush is a waste of time. Also note that very often, these beggars may be part of a large begging syndicate.
Do instead 
There are also various possibilities to consider instead of giving money to beggars:
Very little of what you spend in many countries will end up in the pockets of local people, especially if you choose to stay in expensive hotel chains. Make an effort to spend some where it will go to the poor. Give the street musicians a few coins, buy some flowers from the hawkers, take a rickshaw or a donkey ride. Pick up some local handicrafts. Play the game; bargain hard and try not to get grossly overcharged, but accept that some people need to make a living off tourists. You are probably often going to pay more than a local would, but there is no point in worrying about that.
Make a donation when you visit a church, mosque, or temple. This is a sign of respect for the local religion. In most places, religious organisations (regardless of whatever faults they may have, or whatever theological disagreements you may have with them) do good work among the poor.
If tipping is considered appropriate in the country you are visiting, tip often and tip well. If it is not considered appropriate locally, do not even consider tipping except occasionally when you get truly exceptional service.
Consider donating time and/or money to a local or global poverty reduction program instead of giving change to individuals. Poverty is a complex social issue and begging is a symptom of a bigger problem.
Stay safe 
In some cases begging is a fairly passive activity and in others it can be more aggressive and intimidating. If you feel threatened, walk away quickly and head for a nearby shop or restaurant. Dressing in an understated manner (to look less affluent or more like a local) may make you less of a "mark" for begging, and treating people with respect may help avoid altercations.
Especially in very heavily touristed areas, it may be best to hire a guide or work out a by-the-day deal with a taxi or rickshaw driver. This will cost you a bit of money and puts you at risk of being led to shops that give guides good commissions, but it will likely keep the beggars and touts off.
It is not a good idea to give children money as they are often sent out for this purpose by their parents or other adults, which should not be rewarded or encouraged. In less developed countries, orphans or unwanted children may end up forced into begging by mafia-type gangs, who appropriate their takings and give little in return. In some countries such as India it's not unknown for children to be purposely deformed to make them more profitable to their parents/masters. See the movie "Slumdog Millionaire" for some examples of this.
If you are considering giving a small gift such as candy or pens to children, recognize that this can lead to more aggressive behavior, including physical fights with his or her peers over your well-meaning gift.
In Hindu and Buddhist countries giving alms to monks or nuns is an accepted part of the culture, a religious observance for the giver. Note that you should only give them food, as they are not allowed to touch money under any circumstances. In many religions, especially Islam, giving alms to the poor is also a religious obligation. Note that some non-religious people may have co-opted this approach to profit from tourist "donations".
Buddhist monks 
Buddhism is generally understood to have two main denominations, namely Mahayana and Theravada. Mahayana Buddhism is the dominant form of Buddhism in mainland China, Hong Kong, Macau, Taiwan, Japan, South Korea, Mongolia, Vietnam, Singapore and Bhutan, while Theravada Buddism is the dominant form in Thailand, Laos, Cambodia, Myanmar and Sri Lanka.
Monks in the Mahayana tradition either cook their own food, or are fed by volunteers who cook for them in the temples. Hence they generally do not beg for food. Mahayana Buddhist monks are also not allowed to ask people for donations. Instead, most temples will have a donation box, and it is entirely up to an individual to decide whether or not he/she wishes to donate, and how much he/she wishes to donate.
While it is customary for monks in the Theravada tradition to roam the streets begging for food, they are not allowed to be picky about the food they are given (i.e. they must finish eating whatever is offered to them), and are also not allowed to accept, or even touch money. In fact, offering money to a monk is considered to be disrespectful in most Theravada Buddhist cultures. Instead, monetary donations should go into the donation boxes located in the respective temples, and even then the money is handled by laymen working in the temples, not by the monks themselves. Theravada Buddhist monks are also not allowed to eat solid foods after noon, and therefore have to stop begging for alms before then. In addition, Theravada Buddhist monks are supposed to avoid sexual temptations and are not allowed to have any physical contact with women. This means they cannot accept alms directly from a woman, and will instead put a piece of cloth on the ground for female donors to place their food on, or be accompanied by a layman who will accept food from women on behalf of the monk. Monks are also forbidden from approaching people to request alms, and must instead wait for people to spontaneously offer food to them.
Monks of either tradition also do not sell religious items, and neither will they offer to grant people "Buddha's blessing" in exchange for money.
As many "monks" seen begging in tourist areas are often bogus, by being aware of these customs, you will be able to distinguish the genuine monks from the bogus ones.