My players are free to develop their character's personalities as they like. However, I like them to have some idea of what they're aiming for prior to the campaign beginning. However, I have found that they lean in one of two directions: either they play a slightly modified version of themselves over and over, or they play the same character (often an extremely self-serving mercenary) over and over.
As an aid to PCs creating character backgrounds, and also for my own use, I offer the following quick method for generating characters. The system tends to produce fairly iconic characters, which is somewhat intentional, and also allows a great deal of room for future development, which was definately intentional.
To create a character's background, write four sentences.
The first sentence is the anecdote. This is any one story, fact or memory from your character's past. "I grew up in Rivendell, for a time.", "I dumped a cargo of smuggled goods when I was about to be boarded.", "There's a 24-hour period in my memories that I can't account for."
The second sentence is the quirk. This is any one fact, mannerism or detail about the character's present. “I'm always investing in dodgy businesses in an attempt to make a quick buck.” “I'm constantly whining about how hopeless the situation is.” “I wander the forests as a crazy old hermit.”
The third sentence is the goal. This is something that the character wishes to achieve in the future (preferably not something that can be achieved too quickly). "I want to become a paladin." "I want to wake everyone up, to free them from the tyranny of the machine." "I want to discharge the life-debt I owe."
The fourth sentence is the mystery. This can either be some fact about the character that he doesn't want others to know, or it could be something that the character does not know, but wants to (in which case, it should be something distinct from the goal, or else it's just repetition). "I killed my best friend in a drunken rage." "I want to learn the identity of my human father." "I woke one day with a strange tattoo on my arm, and want to know what it is and what it means."