You'd be hard-pressed to find a fantasy setting that doesn't use magic. Indeed, it has pretty much come to be that magic defines fantasy. A fantasy setting is a fantasy setting because it has magic. Any yet, there are so many different variations on the same basic theme that it almost feels like there is no single thing called magic. However, in reality there only seem to be two variations on magic that I can really find. Within these two catagories there are innumerable sub-variations, but it seems like all magic belongs to these two. Most systems of magic that I have seen actually use some combination of the two, tending towards one of them. So what are these catagories, you ask?
Well I like to define them as 'artistic' and 'scientific' magic. The basic definition of scientfic magic is that of rules. In order to use magic, you need to say the right words, or use the right ingredients, or draw the right magic circle. Just about every video game uses scientific magic, the reasons for which will become apparent. Any system where you choose from a list of spells is scientific. Books can also be like this, the magic in Harry Potter, for example, requires the right codewords, and is therefore scientific. Alchemy from Fullmetal Alchemist is very scientific magic, in my opinion. You have to draw a transmutation circle, and re-combine the thing you are transmuting into something else.
Artistic magic, on the other hand, is about imagination. The magic does what you want it to, without reference to scientific laws. Note that this does not make the magic unlimited. A good example would be 'The Will and the Word' from David Edding's Belgariad. A wizard imagines the effect of his magic, wills it to be, and then speaks a word. If he required a specific word, it would be scientific. As it is, the word is merely a conduit, and any word will do. A wizard could imagine a house burning, will it to be, and shout 'turkey' and the house would catch fire. Artistic magic would be terrible in computer games, and even roleplaying games, as the player has to have something to define the magic by. It has now way to tell what he is imagining. I also find that many films use artistic magic, rather than scientific. In the recent LotR films, for example, what magic there was seemed to be based around what the Wizards wanted to happen. Books seem to use them both in roughly equal measure.
Note also that this doens't mean that scientific magic requires no imagination, or that artistic magic is lawless. This whole discussion has been about clearing my own mind on the subject, and is therefore rather disorganised. Artistic magic has laws to it also. There are limits. In the Belgariad, for example, the magic actually tires the wizard out and they can't use anything that is beyond their own mental strength. Similarly, I'm not saying that scientific magic systems have no imagination. Look at FMA for example, when Edward Elric transmutes stone into the shape of a door in order to escape from a building. There is not 'stone to door' circle that he could draw, it's more that he imagined the stone reshaping itself.
So most systems are a mix of the two. I know this has been a rather serious post, but fantasy is one of my favourite genres, and I wanted to clear my own mind about the magic.