Anyone who watched the ending of [Thor: The Dark World](movie:206462), knows that Loki ended up on the throne of Asgard and that Odin mysteriously and suspiciously vanished. This got me to thinking...what happened to the Allfather? Did Loki do away with him? If so, where is the body? If not, where is he? Also, if Loki did get rid of him, why not produce the body, say he died of old age, and claim the throne himself? After all, no one saw the scene when Thor gave up his kingship. There would have been no witnesses and no one to deny Loki's claim to the throne. These are just a few possibilities about what happened to Odin.
Loki killed him.
This theory is rather unlikely based on two things: 1) Odin is the only father figure Loki ever knew. 2) Loki went to great lengths to save Odin from being murdered by his actual father Laufey. Granted that Loki only did this in an effort to earn Odin's favor, but a guy trying to please someone doesn't generally resort to murdering that person.
Loki threw him in a dungeon.
This is certainly a much more plausible solution. However, this solution is not without its personal risks for Loki. Imagine: a random guard enters the castle dungeons and finds the Allfather incarcerated there. Knowing that even Odin cannot be in two places at once, and knowing that Odin is in the throne room, he will immediately suspect foul play and release Odin to deal with the impostor. He will also sound the alarm and the impostor will be surrounded and dealt with without any hope of escape. Loki is no dummy. He would have foreseen such a situation and made his plans accordingly.
Loki handed him over to the Frost Giants or other enemies of Asgard.
The Frost Giants are certainly not on amiable terms with Odin, and would not quibble over how he came into their hands should he ever become their prisoner. Being that Loki not only IS a Frost Giant, but is also the former king's son and heir, vengeance on the Allfather by the good will of Laufey's successor would seem too good to be true. Doubtlessly, if the Frost Giants did get their hands on Odin, he would not remain alive for very long. Loki could also have handed Odin over to other enemies of Asgard. The problem with this theory is that any enemy of Asgard who received Odin from Loki would immediately attempt an assault on Asgard in order to claim its throne for themselves.
He died of natural causes and Loki kept it a secret.
This theory is plausible, however unlikely. Granted, Odin is no spring chicken, but if he were to have actually died of natural causes, it would be huge news and the entire palace would know it. Also, another problem with this is that Loki, who is supposed to be under guard as soon as he returned from the Dark World, would have to have hidden the bodies of the Allfather and his guards in a place no one would think to look. However, there are very few such places in Asgard, and furthermore, if Loki did hide the body, why does Heimdall not reveal its location and denounce Loki as an impostor?