- Your character background is not a story. Stories have a beginning, middle and, most damningly, an end. A character background needs lots of loose ends and unfulfilled goals in order to be of use to a DM. Write the start of the story, maybe even a bit of the middle, but don't spend time thinking about the end, that's why there's a DM.
- Your character is not the centre of the adventure. It may be tempting for you to have a character with a single minded dedication to a specific goal, often vengeance for dead friends/family/pets. While this is fine for single player games such as one might find on computers or single character focused books, a pen and paper game typically has four or five main characters most of whom have no interest in avenging the death of your pet rabbit.
- Your character is not Jesus. While the DM may choose to reveal at some point that one or many of the party are prophesied saviours of the world, don't write this into your character's background. Aside from the hubris of it, predestination in roleplaying games simply does not work. Ever.
- Your character is not already a world famous hero. Keep in mind the level of the character being created when writing a background. A level one character has probably not commanded armies, slayed dragons, or summoned greater fiends from the pits of the abyss.
- You have to play your character. Don't write up an inquisitive hyper-intelligent wizardly background if you know as a player you get impatient with riddles and just want to fight things. Be honest with yourself about this: playing a silver-tongued rogue can be a lot of fun but if you can't do a passable job in reality the roleplaying is going to be awkward and unbelievable.
- Your background isn't separate from the campaign. By the time you have finished writing a background and discussing it with the DM, you should know the answer to several questions. What kind of personality does your character have? Why would he wander into a dungeon and start killing things? How does he respond to authority? To the classic damsel in distress?
- Your character won't be dungeon delving forever. Often framed as "when would your character retire?" this is the question I find most helpful to defining a character's goals and motivations. Revenge based backgrounds are iffy, because chances are you will exact vengeance, at which point the character would most likely go home and live out his life farming pigs or similar. This is fine if you don't want to keep playing the character. Furthermore the generic "wants to prove his might" non-background a lot of people adopt fails to provide an answer to this question and in a world where there are creatures that could most likely kill the character accidentally, it doesn't promote longevity.
Not only did this give him a reason to go treasure hunting, as well as some incidental revenge from time to time, but his position as a court trained noble combined well with the fact I have a tendency to act as party spokesman when I play. Also, when he finally got enough money, performed a few favours for the crown and got a barony, further adventure hooks were provided by the fact that he was now the sworn vassal of a country at war. I've written characters with more, well, character since then, but often their goals and motivations are a little hazy or are in no way served by going around punching goblins in the face.
When characters have strong backgrounds that give their players clear goals and motivations, being a DM is easy. They don't need to be highly nuanced individuals with complex emotional relationships and subtle personality flaws, although it's helpful if they are, they just need to know what they want to do and why they want to do it. I have run these games in the past, and when having an uninspired week I can just turn to the players and say,
"What do your characters want to do?" From there winging it is no worries. If the players can't answer this question, then their backgrounds don't amount to a hill of beans.