The Aspect of the Blue was one of the more wise of the Dragonflights, and described as the most friendly of them. He was close to his 'siblings' back before the War of the Ancients, especially Neltharion of the Black. You know, before Neltharion went loco.
For many, many years, Malygos avoided combat as much as possible, much like his sisters Alexstrasza and Ysera. He instead relied on illusions and distractions to confuse his enemies, and lure them away from his lair and anything else he found precious. In general, it is thought that he actively avoided the mortal races, but it is rumored that he may have actually helped some of them learn how to use magic to begin with, though that has not been confirmed.
Malygos' generally cheery demeanor came to a screeching halt around the time of the War of the Ancients, the day Neltharion completed his transformation into Deathwing. You see, when Neltharion presented the Dragon Soul to the other aspects and encouraged them to contribute their essence to the disc, it was Malygos that went first and encouraged the others to participate. It was this very disc that ended up destroying almost all of the Spellweaver's dragonflight, and brought an end to the Age of Dragons.
When Malygos' flight had been destroyed, he slipped into a state of mourning, falling into guilt and grief. Having essentially taken part in the murder of his entire flight, his sons and daughters, he was eventually swallowed whole by his grief with that on his conscience, it overcoming him completely.
Later, much much later, ten thousand years later, the Demon Soul was used by the Orcish Horde to enslave the Red Dragonflight and its queen Alexstrasza. We're going to skip all of that killing and pillaging stuff in the middle and go straight to the end of this war, mmkay? Mmkay. At the end of the war, Rhonin and his band of merry men jello wrestled with some Orcs and retrieved the Demon Soul, destroying it and freeing Alexstrasza. Malygos himself played a small role in this, with Krasus, the Queen's consort, using Alexstrasza's power over death as bait to lure him out of his malaise temporarily. To reward the Lord of Magic's efforts, Alexstrasza resurrected much of his flight.
Still, the grief kept a hold on him, and he wasn't in perfect shape physically since his encounter with Deathwing, either. It wasn't until Tyrygosa, one of the few Blue Dragons that remained after the War of the Ancients, returned from her trip to Outland in which she studied and investigated the Nether Dragonflight. Having 'befriended' them, she brought some of them with her to Azeroth, and their nature and physiology had an effect on the Lord of Magic. Slowly but surely, his sanity and drive returned to him. For the first time since the War of the Ancients and the Sundering of the world, for the first time in many thousands of years, Malygos saw the state of the world.
Now, let's be honest. Azeroth is not in good shape right now. There's some nice spots, sure, but half of Kalimdor is covered in demons that the mortal races summoned in and half of the Eastern Kingdoms is either blighted by undead or torn apart by reckless use of magic. Mortals are having tons of fun doing things like summoning Ragnaros and Lord Ahune, former servants of the Old Gods who get their kicks by turning entire zones to ash.
Malygos's last memory combined with the current state of the world and probably a little lingering rage and insanity led him to a decision: All magic users must die. A little crazy, sure, but when you were given life for the sole purpose of keeping magic from being used recklessly, it's probably perfectly logical to him. Still crazy to us, though. Even the Red Dragonflight and the Kirin Tor admit that something needs to be done to reign in how much magic is being used throughout Azeroth. Malygos is just taking it a little too far.
Wrath spoilers below this line folks, so you may want to stop here if you don't like them!
The tactics being used against Malygos in the war between the Blue Dragons and the Kirin Tor of Dalaran are not particularly clean ones, so that isn't helping the situation much. Just outside of the Nexus, the Red Flight and the mages of Dalaran have banded together to stop Malygos through tactics such as murdering his consort, lighting her corpse on fire and doing a merry jig around the flames. They have also enjoyed festivities such as stealing axes from Malygos' soldiers to crack open his consorts' eggs, murdering his children. Of course, Malygos has answered that by enslaving mages and stealing a Red Dragon to use as his replacement consort against her will. Hm.
We don't know quite yet how this will all play out or what the outcome will be, but by the time Wrath of the Lich King launches I'm sure we'll know quite well.