Why beg?

Well they mostly do it because they aren't allowed to buy games(parents).If you try to get a game through steamgifts, the chance of actually getting is near to impossible.(not impossible, but takes a lot of time)

All you have to say is fuck off.

not everyone can afford a game, even during summer sale. or maybe they missed sale on that game. (source: personal experience)

For the same reason why people sit on streets and beg for money. Because it works.

You'll get 100 people saying screw you, but then you'll find one who'll decide to give it to you. Have one guy on my friend list, he begged me whole day to get DayZ. Told him truth - I'm too broke to buy that game. Next day, he had it on his account.

Once read about a guy who made street begging into his work, was able to get $5000 monthly.

i never had a random add for begger, but a couple of guys with whom i've traded later on beg for some game, some card, or some CS:GO skin
I just unfriend them and block them :)

Sorry for bad english.

In my experience, there are generally three types of begging.

1) Begging done by friends or family when they need some temporary help. This is usually limited in both scope and what is asked.
2) Begging done by those who are "down and out." This is usually done out of necessity and desperation.
3) Begging done by people who simply want what you have. These people usually have no real need for that which they are seeking.

Out of those three categories, the third is the most persistent, the most demanding, and the most annoying. They beg in the hopes that their begging will eventually wear you down and you will give them something simply to make them go away. The sad thing about this kind of begging is that it achieves results better than any other method, hence why some people do it.

Professional beggars fit into the third category while attempting to appear as if they are from the second category.