As you probably know, Odin (also sometimes known as Woden or Wotan) was the leader of the Norse pantheon. Well, sometimes, anyway. I believe that Thor and Tyr were sometimes given more authority than Odin, but the popular conception makes the one-eyed All-Father the ruler of the gods. Like modern action figures, classical gods often had a fair number of accessories. In Odin's case, he rode an eight-legged horse named Sleipnir, had raven messengers called Huginn and Muninn, wielded the spear Gungnir, and possessed the self-replicating ring Draupnir.
So why does a super-magical being only have one eye? Well, he gave the other up in exchange for a drink from Mimir's well of wisdom. See, the Norse gods didn't have quite as easy a time of it as the deities of some other cultures did; they had to give things up in order to obtain the power and intelligence that other gods start out with. Odin also hung himself from the World Tree Yggadrasil for nine days and nights with a spear in his side, in order to obtain knowledge of powerful runes. He was all about self-sacrifice in order to better himself.
So, with Easter coming up soon, I have to raise the question as to whether Odin's self-sacrifice relates to Jesus' in any way. They both hung on a wooden object in order to achieve something divine, and the Gospel of John even mentions a spear (later known as the Spear of Destiny) being used by the Romans to pierce Jesus' side. I'm not sure there could really be a direct connection; was there even any communication between Scandinavia and the Middle East in the early AD years? Perhaps the similarity can be chalked up to Carl Jung's collective unconscious, and Joseph Campbell's idea that all myths cover the same basic themes. After all, the Norse weren't the only culture to have a World Tree, and the idea of a tree being a bridge between Heaven and Earth is a pretty basic one, and Jesus' cross was sort the equivalent of a tree for the Roman era. And we can't forget about Siddharta Gautama achieving enlightenment by sitting under a tree (fortunately for him, he didn't have to physically hang himself from it, but it's a similar idea), and I believe I've even heard legends of his being attended by an animal during his meditation, just as Odin was fed by the squirrel Ratatosk. Perhaps it's all just the human desire to see patterns in stories that really aren't that similar. I don't know, and I would appreciate any more information or theories that you might have.
Despite being the ruler of the gods, Odin was most closely associated not with Zeus/Jupiter, but with Hermes/Mercury, apparently because Odin and Mercury were both the ones who led the dead to the next world. That's why the Latin Mercoledì became the English Wednesday. So that's one way Odin lives on, and he's also a fixture in popular culture. He appears as a summoned being in many (possibly most) of the Final Fantasy games, often using Gungnir as a weapon. Oddly enough, FF6 offered the ability for Odin to turn into Raiden, a Japanese thunder god. You'd think it would be more likely for Raiden to be associated with Thor, but I'm not sure he ever appears in the FF games. Odin was also a significant character in Douglas Adams' The Long Dark Tea-Time of the Soul and Neil Gaiman's American Gods (which I've read most of, but still need to finish). I didn't really think the latter's portrayal of the All-Father as a backstabbing hustler really worked, but maybe he'd just been spending too much time around Loki.