Here's what I think magic "should" be like in DF once it's all complete:
GENERAL: It varies from world to world, from civ to civ, maybe even a bit from magician to magician. In some places you can't swing a black cat without hitting something magical, and in others magic is regarded as superstitious nonsense. Some individuals should break the general pattern of the area, whether by practicing a forbidden school of magic, or by insisting that magic doesn't exist, or by searching for magic in an athaumatological land.
Also, magic should always have a cost that makes you think twice before using it. Maybe it has a risk of summoning demons to attack you, or maybe it requires a lot of energy (your fireball fried most of the bandits, but if you fall unconscious that last one is going to kick your head in), or maybe it requires a rare reagent, or maybe...the costs should also vary from type of magic to type, and from world to world.
DWARVES: Magic is too fickle to be trusted, think the dwarves. They might implement it in small ways, like a forge powered by an everburning flame or magical weapons, but mostly dwarves use steel and stone. The exception is religious magic; dwarven priests are good at excorsisms, healing, and perhaps a few other minor things, but these solutions are usually expensive and time-consuming, which is why many less-devout dwarves prefer conventional methods, like burial and medicine.
HUMANS: Humans are the least-fleshed-out race in DF. I think that humans should dabble in all kinds of magic; they aren't as powerful as elves, but make up for it with their determination and versatility. They might bring some magical goods to trade with dwarves.
ELVES: The most powerful race magically, but also the most focused. Elvish magic mostly focuses on life and growth, but some druids can guard the forests more violently by animating trees, causing animals to grow and become viscous, and the like. They almost never learn spells relating to fire, stone, or death.
GOBLINS: Goblin magicians love fire magic and other destructive spells, but most goblin magic revolves around summoning and serving demons. Their servitude might lead to them being blessed somehow, or at least to being able to rain destruction down on their enemies. Goblins are usually not as powerful of magicians as elves, kobolds, or even humans, but demons enhance this, and if a goblin civ's patron demon decides to visit your fort...good luck.
KOBOLDS: Kobold magic should be mostly shamanistic. Kobolds can transform into small animals, or sometimes bigger ones, perhaps bring minor natural disasters like small floods and lightning strikes down on their foes, and direct animas to cause distraction elsewhere. Shamans can also request animals to help them by providing meat; this coerces the animal to come over and lie down, where the hunters kill them happily. And so forth. Not much powerful, but if a few kobold shamans come onto the map, prepare to feel the wrath of koboldkind...
ANIMALPEOPLE: When they get more fleshed out, animalpeople should be able to control other animals of their kind, and similar animals (brown recluse spidermen should be able to command cave spiders, for instance). This can range from amusing (cave swallows coming and nipping dwarves' noses before being caught by cats) to deadly (a platoon of giant badgers shredding their way through your fort). They might also have some shamanism like the kobolds, but not as strong.
OTHER SAPIENTS: Varies. Trolls are too stupid to use magic, ogres might have a bit of innate magic from their dark surroundings, dragons can learn and teach spells to magicians of the smaller races who appease them, etc.
ROGUE INDIVIDUALS: A wide variety of possibilities. Like necromancers do now, some people might try to search for secrets, distancing themselves from society in the process. Other times, a "normal" magician might discover a secret, then flee into the wilderness to keep it from being discovered. Wizards might be banished from society after their dark experiments are discovered. Et cetera. These individuals may or may not want to use their power to take over their old country, and may or may not succeed.