What makes a good backstory

A good backstory needs to show that you have thought out your character, that you understand him/her and know how he/she thinks. It should also provide your gm with an understanding of who your character is and how he/she got that way. Lastly a good backstory should provide your gm with material to work into the game is the gm so desires (I like the odd chance to throw a character's family into a game personally).
So a good backstory needs to be long enough to do all of this, but still short enough that your gm won't quit reading half-way through. I usually recommend (or when I gm require) a minimum of one page and a maximum of three.
Your backstory should answer the following questions:
(1) Who is your charater?
(a) What are their defining features both in appearance and personality?
(b) Where are they from?
(c) What is important to them?
(2) What is your character like?
(a) How does he/she act when they are alone?
(b) How does he/she act in a group?
(c) Is he/she good or evil? sane or insane? friendly or hostile?
(3) Why is he/she the way he/she is?
(a) What defining events in his/her life made him/her what he/she is?
(b) What purpose does he/she believe he/she serves (if any)?
(c) Who were the influential people in his/her life?

You should focus on the details of specific, and particularly important, events is your character's life. You should also choose an appropriate age for your character, baring extremely special circumstances a lvl one character should not be a fifty year old man and a lvl sixteen character should not be an eighteen year old girl.

You should avoid attempting to roleplay your character in your backstory, a backstory should read more like a history text than a fiction novel. Whenever I see character script in a backstory it tells me that the player is trying to fill up space and look like a good roleplayer but not that they have completely thoughtout the character they want to play.
Don't feel like you have to account for every minute of your character's life, unless it was a lifechanging event no gm cares what he/she had for breakfast on the morning of his/her sixteenth birthday. However, you should try to account for every year of the characters life, a statement like "He then spent three years apprenticed to one of the tower masters of Luskan" fills in a three year period with a single sentance.

Here is an example of a backstory I wrote for one of my characters:
Epimonius Fith was a troubled child. He grew up in a village a few days south of Silverymoon. Fith's strange powers, which appeared in his infancy, combined with his illegitimate heritage, made him an outcast among the villagers. Only his mother knew his father's identity, and she wouldn't tell anyone; not even him. This, along with his innate magic, led the villagers to conclude that he was sired by a demon, or something equally grotesque. In fact the only person who paid Fith any real respect was a young girl named Marta Fied, who was his only friend from the age of five on.
By the time Fith was fifteen he was completely in love with Marta, and was convinced that she was equally in love with him. On the evening of her fifteenth birthday Fith snuck to her house, intending to convince her to run away with him. Instead of a quiet celebration Fith found that the household was in the midst of a large wedding party, Marta had been betrothed to another village boy that very day. This realization broke Fith and, in his rage, his powers manifested in a large fireball which blasted into the house. Fith, realizing what he had done, ran into the burning building in an attempt to save Marta and the partygoers. He managed to save a few members of Marta's family, including her father Ildes Fied, and the right side of his body was badly burned in the process. However the majority of the attendants burned to death, some twenty-seven people, including Marta.
The villagers, not knowing that Fith had started the blaze, treated him like a hero. Fith was finally receiving the acceptance that he longed for, but his could not help but watch Marta's father as he mourned his family. The guilt he felt ate at him and at the same time; perhaps because of the guilt, perhaps because of the outpouring of magic he had shown; he started to dream of an ancient red dragon and of an all-consuming flame. It was not long after he had healed that Fith decided to leave the village, the guilt and his continuing dreams making too difficult for him to accept their hero worship.
Fith spent the next three years traveling the sword coast working intermittently as a mercenary, guard, and briefly as an assistant to a powerful wizard in Waterdeep. During this time his powers grew, as did his skill with weaponry, but the dreams grew worse. The ancient dragon urged him to embrace his birthright and the power that came with it. Just as he began to tire of his position as an assistant Fith received an invitation to attend a dinner at Castle Ravenloft. Hoping to gain the favor of the Castle's lord, and perhaps a place in his court, Fith accepted and found himself joining a group of adventurers who had also been invited.
Fith and the others were lured, and trapped, in a magical world within the castle. A powerful demon named Kratz (a servant of the demon-lord Gratzz), was trying to turn the group to the worship of his master. The innately evil character of the pocket plane catapulted Fith's dreams into full, waking hallucinations and accepting the power and heritage promised by the ancient dragon proved the only way to avoid falling prey to Kratz's schemes. Fith discovered that the blood of an ancient, and powerful, red dragon flowed through him. Fith took the name Ogon, a word which, in the language of the citizens trapped within the pocket plane, meant firebringer. He drew upon this power when confronted with Kratz's minions and eventually broke free of Kratz's pocket plane.
Fith, now Ogon, was the only member of his party to escape Castle Ravenloft after just over a year trapped in the pocket plane within the castle. He traveled east and spent the next twelve years journeying in and through Thay, Rasheman, and further into the Anarouch desert. Supporting himself as a mercenary, and occasionally as a brigand and thief, Ogon fought for both the Zulkir's of Thay and the Witches of Rasheman during his travels. Overtime he grew in his power and understanding and became a half-dragon.
With the power of his birthright he has recently turned his mind toward achieving immortality and so has returned to Thay intending to learn the secrets of undeath from the Red Wizards of Necromancy. His current goal is to turn himself into a lich to gain the immortality that comes with it and then travel the planes in search of the ancient dragon who still haunts his dreams, demanding that he burn the worlds of man, demon, and celestial alike.
While this background is, actually, a little short for a 16th level character it includes all of the elements I listed above. You can see from reading it that Ogon has struggled with his morality, but seems to have ultimately landed on the side of evil, though he may still lean toward neutral. He is also more than a little insane, though it is clear that his dreams and visions are of an actual being they have driven him over the edge. This background also give an idea of his future goals.