In the Final Fantasy series, Odin is a summon. He originated in Final Fantasy III for the Famicom originally as a boss, though after defeating him he would be added to your list of summons. He could also be purchased if you were not able to defeat him.
In Final Fantasy IV, the King of Baron is represented as Odin after being killed. The summon will be added to your list after you find and defeat him in the basement of King Baron's castle. According to a book, the king was victorious in battle, only to be struck down after a bolt of lightning hit his raised sword. Oddly, the characters' weakness is thunder. The only character in the game capable of summoning Odin is Rydia.
In Final Fantasy V, Odin uses his sword to slice enemies in two if they are not immune to instant death. Otherwise he'll use another powerful attack titled Javelin. The only way to have Odin join your party is if you can defeat him in less than one minute in the basement of Bal Castle.
In Final Fantasy VI, Odin can be upgraded into Raiden by making the queen's statue cry on his magicite. In the game, Odin was the guardian of the castle 1,000 years prior to the game.