I expect a character who has moved beyond the physical realm as we understand it. To allow for characters of this magnitude of power, I instituded a Tier system in my universes. When a character reaches 20th-level, they are capable of traveling through a "gateway" of sorts which links to a higher state of reality. A Commoner in the Second Tier is CR 20; a greenie adventurer native to that world is CR 21. This may come from multiple HD or templates. The "weaker" creatures of the Second Tier would be those such as Tarrasque clones (they're everywhere in the Second Tier), great wyrms, HD-advanced balors, etc. When a character reaches ECL 40, they are capable of moving to the Third Tier; at 80, the Fourth; at 200, the Fifth. While there are always those in any given Tier with knowledge of one level higher, no one knows if there is a power greater than the Fifth tier, as even a mighty ECL 1,000–whose power is beyond anything a Fourth Tier dweller can begin to comprehend–knows nothing of the powers greater than them. It is a popular (and frightening) theory, however, that the Tiers continue infinitely upward.
So what could a 1,000th-level character do? With a thought, destroy the entirety of any lower Tier. The character is theoretically powerful enough to wreak mass devastation upon the Fifth Tier, but nowhere near enough to utterly destroy it.