Well, in general every ongoing universe has characters who are defined as totally all powerful at one point or another. So any serious discussion needs some qualification.
It's also important to note that in general comedy characters should be considered seperate from serious fare. Dragonball Z for example is a satire, and the power level it's on is intended to be funny, even if it manages to stay fairly consistant within it's own mythos. Putting say Goku up against a character who no matter how cheeseball they might have been at times is trying to be taken seriously (like say Superman) doesn't work... because as people have pointed out Goku is by definition absurd (he dies, goes into training in heaven like a martial arts movie, is inevitably resurrected and comes back stronger).
It's also debatable because especially when dealing with the Western concept of heroes, you have a LOT of characters who have unbelievable power but for one reason or another hold back and don't use it (knowingly or otherwise). Some eastern/anime type characters HAVE indeed emulated this, but it tends to be a bit more common, with the characters oftentimes being the exact opposite of the whole "Spider Man" thing and using their power with incredible irresponsibility.
In general if I had to pick a single character (as I did in a similar discussion) I'd pick Thissaly from the DC Universe. Really the only reason she runs into problems is because of her arrogance. All this discussion about destroying universes and such is nice, but she can do that quite easily. She just prefers to sit around with her bunny slipprs, drink tea, and read poetry. When she cuts loose she's usually playing on the level of universal concepts that define all reality. Gods generally don't mess with her (though many hate her guts for various reasons), it was defined in one comic that she learned how to "topple the pillars of heaven and hell" and basically destroy all reality. Goku, The Spawn Mythos, The Beyonder as originally defined (the incarnation of an entire reality as a being), she's more powerful than any of that stuff. To really "get" Thissaly you have to be like Dream, but even then she's been able to single handedly cast spells on that level, and frankly most of those beings either leave her alone (and she's basically on a first name basis with most of them).
She's pretty much #1 on my list simply because unlike other characters who were redefined, had their power "potentially", or for some reason lost or do not use it, she has remained consistantly on that power level... which is generally fine given that the stories with her while fairly serious usually take place on such an absurdly high cosmic level. Usually involving such concepts as (from Sandman where she was created): by extremely dumb luck, cosmic forces happen to convege on the residents of an apartment building where she happens to live, and just wants to be left alone.... causing her to get irritated.
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If I have to pick a character for generally absurd universes I generally go with Bugs Bunny. Laugh if you want but the guy is totally indestructable, and reality surrealistically alters itself to his benefit. Not even Goku could defeat Bugs Bunny. Even if he destroyed a planet all that would happen is Bugs would poke him on the should from behind and go "Eh, what's up Doc?"