Superman, as orginally described, was invulnerable. Having a hero with superpowers that are too strong makes for a boring story, because a good story needs conflict. There are several ways of handling that, of course.
1. Kryptonite weakens my powers
According to some accounts, kryptonite was invented specifically to make Superman less invulnerable and boring (Paul Fairchild explains why this was a bad decision). Kryptonite, of one kind or another, is a classic solution to the problem of an overly strong superhero which, to some extent, has been used by multiple authors. It can be overused, however. If your superhero is always weak, why have such a character at all? A better variation of this approach is for the protagonist to carry his or her own metaphorical kryptonite inside, as some kind of “fatal flaw.”
2. My powers come at a heavy cost
This is one of the easiest ways for an author to ensure that his or her character does not overuse their superpowers. These superpowers may cause pain, coma, physical harm, or other damage that enforces a break between uses of the superpowers. For example, the psychic Greg Mandel in Peter F. Hamilton’s Mindstar Rising and its two sequels suffers severe headaches when his powers are used to excess. Variations of this approach are used in a number of fantasy novels.
3. My powers disturb or frighten me
A good example of this option is Doctor Who, in the eponymous TV series, who often needs to be talked into taking action. The advantage of this approach is that it produces a great deal of interesting dialogue on why the superpowers are disturbing or frightening.
4. I am still learning to use my powers
This option is particularly common in young adult fiction. It allows the author to have an attempted use of powers either succeed or fail at any point; but this makes sense with a young protagonist. The young magician Pug in Raymond E. Feist’s Riftwar Saga is a good example. So is Luke Skywalker in the original Star Wars movie trilogy. To some extent, Aragorn in The Lord of the Rings can be viewed as having a combination of (3) and (4). But, however the author does it, I think that some limitation on superpowers is essential for a story to remain interesting. What do you think?
Scientific Gems 
Hi Tony, again it turns out we like the same authors. I always found it significant how similar the stories of Pug and Edeard in Hamilton’s Void trilogy started. Pug met ever stronger adversaries where Edeard finally got lost in his endless endeavours to shape the world into perfection. Different ways to deal with heroes with super powers.
But I have to say that Feist struggled with the powers of Pug because he definitely was not very consistent in weighing them against the challenges he was facing.
I get the feeling that Feist kept making Pug more powerful as the threats kept getting bigger; and then Pug eventually became so much of a superman that Feist had to give him a reason not to be involved.