For the record, this is my magic build. I named my High Elf Palpatine. Once he enchanted enough equipment to give him free Destruction magic he liked to madly cackle while blasting his foes with unlimited power.
There are enough perks left over to invest more heavily into one of the magic trees, or into a non-magic skill tree. Destruction is the priority. Obsessively level Destruction before all else. For crowd control pick either Illusion or Conjuration to dump a lot of perks. Personally, I prefer Illusion. Atronachs work best outdoors, and zombies don't start to shine until Conjuration is almost maxed out. With Illusion, mobs tear each other to pieces and the last man standing is weakened enough that you can probably one shot him.
I call this build a pure mage but you'll see I didn't put any perks into the mage armor talent. Mage armor is okay, but ideally you shouldn't be getting hit at all. You have enough perks to max out your mage armor or drop a few into light or heavy armor.
I am a true Nord barbarian because pure mage is probably my least favorite archetype. Pretty much all fantasy games that allow you play a mage scale in the same way: at the start of the game you're lovely and get one shot by everything, and by the end you're a physical god that no enemy can touch anymore. Destruction, unlike weapons, does not scale. This isn't a problem once you've enchanted your gear for free Destruction magic, but it makes dragon fights especially anticlimactic. The Impact perk in the Destruction tree staggers all enemies when you dual cast a spell. If your magic is free, then battles become long drawn out affairs of poking the bad guys to death. You keep them in a permanent stunlock until they fall over dead.
A lot of people think mages are underpowered in Skyrim. I'd disagree with that. Pure mages are absolutely the most difficult builds early in the game before you get your skills dialed in. In contrast, assassins are good to go about an hour in, and warriors can hold their own right out of the gate. I played as a pure mage to get the trophies, and haven't played another one since.
EDIT, 7/26: I see that my Skyrim builds tend to be my most popular posts. If you're new here, welcome. Come for the video games and stay for the crimethink.
EDIT, 8/20: And to be fair, a pure mage is your best bet for breaking the game into a thousand pieces.