Golden Age Version
Jim Corrigan was cop that was murdered. But, his spirit was denied entrance into the afterlife. He returned to Earth as a undead being and was assigned to be a superhero by "The Voice" (God?). As the Spectre, he was seeking bloody vengeance against Corrigan's murders. He founded the Justice Society of America.
Silver Age Version
This version was some what rewritten from his Golden Age counterpart. He was still an avenging spirit, but he was also nearly omnipotence.
Bronze Age Version
Again, the Spectre was some what rewritten. Here, he used his power in gruesome ways, giving "poetic-justice" to criminals: melting him like wax, turning them to glass and then shoving off a cliff and etc. Many fans were unease by this version of the Spectre, so a reporter called Earl Crawford (who also found the Spectre disturbing) was introduced. He fought in the Crisis on Infinite Earths.
Modern Age Version
This version had both elements of an avenging spirit and a brutal police man. It's revealed the Spectre wasn't actually Jim, but a fallen angel. He possessed Hal Jordon's dead body to stop the fear-entity Parallax. In the Day of Vengeance storyline, he was tricked into causing havoc among magic-users. Later, the Spectre got a new host (he left the Hal Jordon body): Crispus Allen. In Blackest Night, a Black Lantern ring turned Crispus into a zombie (with the Spectre still in it!), but Hal Jordon (somehow alive) saved him.
Powers and Abilities
The Spectre can do almost anything, when he has a host. However, he's venerable to strong magic and needs a host.