Note: I'm recycling! This post originally appeared in August 2011, back when no-one was looking...
I've always enjoyed reading stories where characters have powers, but I especially enjoy it when those powers are somehow unusual or limited. In some story universes, magic exists and anyone (or certain people) can learn to manipulate it, while other stories exist in our world, but with magic accepted here too.
I remember being really impressed when I first read Sarah Addison Allen's Garden Spells, in which a particular family in an American small town is known locally for having certain abilities, including unusual and very specific gifts such as: knowing the right place for everything and everyone; being able to create everyone's perfect hairstyle; giving people strange items that will become essential later (she can't 'see the future' as such, just knows that so-and-so is going to need a small hairbrush, chewing gum or a mirror). This small-scale magic is a pattern repeated in her other books that I've read too, and part of the delight of reading them lies in discovering these quirky powers.
I think that in many ways it's more interesting to give a character (or a family or other group of characters) specific and limited powers, rather than more general ones. It all depends on the world you've created, of course, and the genre you're working in. High Fantasy, for example, arguably requires magic to be a more general power, which can be used for good or ill in a number of ways. I suppose that, in this as in many other aspects, writing in sub-genres allows more freedom to be a bit quirky with it.
What magic-using stories have you enjoyed? If you write using magic, do you use it as a broad force, or in a more specific way?