It really depends on the character, and the role they will be playing.
As has been pointed out already, a good general principle is that the more time you are going to be spending with a character, the better it is to give them a backstory. Unless they are supposed to be an enigma to the reader, in which case the mystique of the character can actually be ruined by giving them a backstory.
There are also cases when you will get your best effect by not giving them any back story at all. One way to make an evil villain or minor antagonist terrifying is make their backstory a mystery - this gives the reader nothing to cling to, just the absoluteness of their malice. The Joker in The Dark Knight is one of the most terrifying villains I've ever seen on the screen, in part because the moment you think he's given you a backstory to explain his scars, he then gives you a different one.
So, I think what you ultimately need to consider are:
Is this character supposed to be sympathetic?
Is this character supposed to be mysterious?
The first leans more heavily towards creating a backstory, while the second leans more heavily towards not creating a backstory.
But, as I said, it all depends on the character and their role in the story.