A good character is more then the sum of the numbers of their character sheet, they have personality, motivation, and a life of their own.
A background lets us know something about that personality, for the player this helps them get inside the character's head and really roleplay, for the GM it provides an insight that allows him to take hold of the character's motivations a drop relevant plot directly in front of them.
For the typical D&D game the GM needs to provide little more motivation then "There be gold in them there dank dungeon", but many games need a little more than that.
This document is an attempt to provide some gentle prodding that can aid players in creating backgrounds for their characters. It takes the form of a series of questions, which should be used as food for thought.
Don't try to answer them all in order, read through them first. Any answer that leaps to the front of your mind should be filled in, anything else, don't worry about at first.
Then go over them again, trying to fill in the gaps. Don't be afraid to jump back and forth, and don't be afraid to change answers you've already given.
Don't worry about answering every question, the more you answer, the more material you'll have to work with, but you don't need to answer everything to produce a respectable amount of material.
Once you have enough information down that you are happy with, start arranging it in chronological order and writing it up in prose. Before long you should have a respectable character background.
Its usually helpful to describe a number (half a dozen is good) of people who are "important" to the character in some way. Often its helpful to include):
Places are important, they are almost characters in their own right, and characters care about them. A home might be threatened, or haunted for example. They also offer further insights into the character - "Who lives in a house like this?"