I've heard even non-comic book fans ponder who would win in a Superman vs. Thor match up, or a Superman vs. Hulk battle?
The answer is ...
It has been done before.
Superman beat Thor up pretty good in a DC-Marvel crossover comic some years ago, before the rest of the Avengers also teamed up on Superman.
Superman has also faced The Hulk at least 3 times in past comics. The most recent battle was one where the Man of Steel finally won, but stated it took all he had.
There's also a classic DC-Marvel crossover comic book cover where Superman is holding Thor's hammer and Captain America's shield as the lead defender of the universe against a huge cosmic threat