Character Backstory

In roleplaying games, I get to create my character, but of course some things about that character's background are going to be decided for me.  I might decide to play an elf, but that elf is going to be from Treetown, because that's where all the elves are from.  But did my character love or hate Treetown?  What did they do there?  Why did they leave?  That might (or might not) still be up to me.

As someone who likes to create lots of different characters for lots of different playthroughs, I've found there's an interesting middle ground to this.  Too specific a background is hobbling, but too vague and I have an equally difficult time coming up with a character.

For example, In Dragon Age II the player character always comes from the same place with the same family.  They might be a warrior or mage and might react entirely differently to things due to entirely different opinions, but I always have a hard time imagining lots of possibilities with such a singular background.  It's great that the game offers your character plenty of choices, but without the excuse of varied backstories, I've had a hard time coming up with many different characters to explore them all.

On the other end of the spectrum is Fallout:  New Vegas.  The player character is a courier and no further background is given (until expanded content, anyway, and not much then, as far as I understand.)  This leaves a ton of options for character backstories, as there are plenty of reasons for someone to become a courier.  However, I've found that I miss at least a little more background.  Without something more to go on it's difficult for me not to fall into the same old character ruts.

A good middle ground for me is something like Mass Effect.  Mass Effect offers two selections from three background events (so six total variations) for your character.  Yet these events are vague enough I could come up with hundreds of characters.  If my character grew up in the slums of Earth, are they a hardcore alien-hating gangster, or just curious about exploring the far regions of space?  Up to me, but at least I know where my character came from.

This is, of course, just my preference.  Perhaps you find the more details the merrier when it comes to your character's background, or maybe you hate the idea of anything else being imposed.  Or maybe you don't give a rip.  What do you think?