In Stargate, he dies. He and his entire race blow up their own homeworld to keep it and themselves from the Ori, after bequeathing all the knowledge of the Asgard on the Tau'ri, referring to us as "The Fifth Race" (see Alliance of Four Races - Alterans (Lanteans/Ancients/Gatebuilders), Asgard, Furlings, Nox). They do so because they cannot "ascend" as the Alterans did because they screwed up their own genes by trying to prolong their lives forever, and now they're screwed by a genetic disease. But, we get cool lasers. And time dilation devices. And lasers. And superfast intergalactic engines. And lasers. Oh, and beam transporters. And did I mention lasers?
In Norse mythology, he will die. Thor pwns. That's the point. He fights the good fight, and knows he's going to lose, but fights it anyway. That's what makes him great. That is the entire point of Viking mythology