In fact, Superman and Batman first crossed over on the Superman radio series in 1945, years before they first crossed over in the comics. The radio show often brought in Batman as a guest hero when Superman's portrayer Bud Collyer was on vacation. Superman and Batman have been part of the DC Universe in the comics for as long as it's existed as a continuous universe. Of course they were founding members of the Justice League of America in the early '60s and have usually been part of its roster ever since. They also appeared as core JLA members in Super Friends throughout the '70s and early '80s, and in multiple different Justice League animated series and movies from the '90s through the present. Of course, the different adaptations in which superheroes appear are all different "universes" retelling the story in different ways, so yes, there have presumably been filmic universes in which one hero existed but the other didn't. It's a safe bet that the version of Batman from the Christopher Nolan films exists in a universe without a Superman. On the other hand, the George Clooney Batman did mention Superman in Batman and Robin, and I think the previous film alluded to Metropolis. And there's a passing reference to Gotham City in Superman Returns.