Marvel's biggest superhero teams came to blows in the epic, multi-series crossover Avengers vs. X-Men (a.k.a. AvX) in 2012, but the two franchises are owned by different studios - Avengers at Disney, X-Men at Fox - and it's unlike they will ever want to share the profits on what could be the biggest movie ever produced.
Warner Bros. owns the rights to both Batman and Guy Gardner, Earth's jerkiest Green Lantern, but the odds that they'll actually put Gardner in a movie - especially when Hal Jordan, John Stewart and Kyle Rayner are more popular - are pretty slim. So the iconic fight in which Batman took Guy out in a single punch will, sadly, probably never make it in front of the cameras.
In one of the great early Marvel superhero fights, Sub-Mariner emerged from Atlantis to destroy humanity, and only Daredevil was around to stop him. Outmatched in every way, Daredevil fought until he collapsed. Sub-Mariner respected his fearlessness so much he figured humanity was worth sparing. Both characters are owned by Marvel, but the studio is still trying to get the rights to Sub-Mariner sorted out after the character was originally optioned by Universal.
The strongest, most misunderstood monsters in the Marvel Universe have a long and storied history of beating the crap out of each other. Who is strongest? Who is toughest? We may never know in live-action, since Fox owns the rights to Fantastic Four and Marvel's got The Hulk under their own banner.
It took decades for Marvel and DC to set aside their differences long enough for a comic book crossover between their competing superhero universes, and it will probably be at least that long before Marvel Studios and Warner Bros. seriously consider letting Batman fight Captain America, Superman fight Thor, and so on and so forth.
The teenaged clone of Superman and Lex Luthor repeatedly fought an alternate reality Superboy who was a dangerously insane mass murderer. Yeah, even though Warner Bros. obviously owns both Superboy and Superboy Prime, the odds that we'll ever see their weird, epic, head-exploding battle on the big screen are extremely low.
Aliens have challenged Earth's mightiest champion, but when Superman steps forward, the legendary boxer Muhammad Ali points out that he's not really from Earth. So they fight to prove who is truly the greatest, and sure enough, Muhammad Ali kicks Superman's ass (in all fairness, the hero's powers were deactivated, and he put up a good fight). But it seems highly unlikely that Warner Bros. will decide to send Superman back in time to fight Ali in his prime, doesn't it?
In the Marvel Comics, fighting Wolverine is like a rite of passage. He's had iconic tussles with The Hulk, Captain America and Spider-Man, and was thrown head-to-head against any rookie hero that the publisher wanted to prove was a badass. But Wolverine is owned by Fox, who only have the rights to the X-Men and the Fantastic Four. We will probably never see Wolverine fight an Avenger in a live-action movie, and that sucks.