Rarely.

I have the same problems with omnipotent characters as I do supernatural:  there are rarely built-in rules governing their actions.  At best, you get a thoughtful story that explores the human condition as the protagonist sways the omnipotent antagonist to another viewpoint or to at least see things from new angles and consider them.  Another frequent thing is the opposite who balances things.  Those end of being metaphors about how too extreme a viewpoint tilts reality into danger and that balance is better long term. 

Fantastic Four introduced Galactus in a story that was essentially the End of the World, as God comes to render judgement upon the Earth.  The Silver Surfer ends up being a wrinkle in things, as he comes to see that Galactus' need to consume destroys other living things.  Meanwhile, the Watcher introduces an opposite to Galactus, in the form of the Ultimate Nullifier and apocalypse is avoided.  However, Galactus became less interesting, to me, when he reappeared.

You have the favorite Trek trope of super computers that are undone by questions that don't have binary answers.  You also had the gimmick of the proto-Q, The Squire of Gothos (later retconned into being of the Q race), who turns out to be nothing more than a powerful child, playing with toys, until disciplined by his parents.

It's all in the metaphor you want to use; but, they've pretty much been done to death and rarely is the omnipotent being either truly omnipotent or relatively alien.  Something that powerful and beyond our norm should be remote and alien to us; but, so few writers ever really achieve that.  Arthur C Clarke's 2001 is one where it kind of works.  The monolith represents a type of omnipotence and we struggle to understand its actions or influences, mainly because we have to interpret them for ourselves, though Clarke's novel version (vs the film script) clarifies some elements more than the film (such as Moonwatcher, the man-ape who discovers the concept of "tools").  2010 spent more time explaining what was happening; and, though I still liked the story (and the film), it feels less trusting of the audience.

The best use in comics is as a metaphor for the concept of a supreme being and exploring what happens when the character "meets its maker" (some more literally than others).  Problem is, if it was successful once, it must work 12 times, right?

Actually, I think that's part of what made Dr. Manhattan so interesting in Watchmen. He didn't ultimately solve everything with his power, nor did he have an equally powered up adversary. His gradual distancing from a "human" way of thinking was a more "psychological/evolutionary" (if you will) development, and I think some genius on Moore's part.

As a fan of cosmic Marvel and cosmic operas in general, this is probably what we be the deciding point about whether I like a story overall. Avengers: Celestial Quest fell prey to this big time. Where I enjoyed page and after page of the six issue mini, and then it fell flat inside 2-3 pages right at the end where the "solution" to the cosmic annihilation was so unreal to both characters that it almost ruined my desire to read it as much as would had the ending been either left open or better resolved and realistic of the characters involved in the solution.

There's been other cosmic operas in comics over the years that have feel to this end. Be in a back up story in a comic or a major event. And for me that seems that the writer never had a plan and just was writing as they went along, realized they were running out of pages and wrapped it up real sloppily. But the Celestial Quest was the one that stood out the most as it had Thanos act in a way that was contrary and completely out of his character.

The limits of TV Hulk's power fluctuated from time to time. For instance, in the pilot, he flipped Banner's car, single-handedly lifted a large concrete pillar, and tore his way out of a chamber structured for undersea pressures. In a 4th season episode, he stopped a tank from running over him, and in another, pulled down a helicopter. It seemed his power grew as the seasons passed, but it still felt realistic because--as you note--he was not like the comic Hulk who is powerful enough to kick tanks into orbit.

I agree that omnipotent characters do, and should have a limited shelf life. Familiarity breeds contempt, and as far as I'm concerned massively powerful characters should be seen very sparsely (Thoth-Amon under Roy Thomas) or their activities should remain a mystery (the Celestials under Kirby, as observed by berkley ).

Lovecraft's cosmic horrors come to mind. You rarely, if ever, see them at all; you have little idea of what they want, but they are all the more terrifying for it.

This thread is giving me Beyonder flashbacks. 

Also, and maybe this sounds dumb, but if a person has 111 different abilities. And they are battling. They might forget that a certain attack or method would work better in the moment. Fighting other superbeings is a high paced, fast thinking event. You might overthink or you might forget of an attack or ability or strategy you have.

A human example...I have a bunch of tools in a shed and scrap pieces of everything. Last year, to trim my hedges, I used my ladder and leaned it into the hedge which was precarious and probably dangerous at times. This year, upon digging through the shed, I found a piece of wood I forgot I had used previously that was perfect to strap to the ladder top, distributing my weight more evenly and making it easier to do the job. Last summer I rushed to do it one day before going away on holiday and completely forgot about this added piece that made the job easier and safer.