Iron Man vs. The Hulk in 'Avengers: Age of Ultron'
Although Iron Man well knows that The Hulk can survive great blows to the head and enormous drops from great heights, he still feels that putting on a giant robot suit and fighting with him in the streets is the best way to incapacitate him. We know The Hulk can be strangled, so you would think strangling would be a priority. But no, Iron Man punches and punches. The thing that ultimately works is The Hulk sees that he was causing destruction. Of course then Iron Man punched him in the head, and the scene ended. Perhaps a punch was the solution, although I took from the scene that it was Hulk's melancholy that ended the fight. He gave up. He wasn't knocked out.
Any fight in 'The Avengers'
The fights in Avengers VI: The Avengers are more or less, functionally speaking, meet-cutes. When the three heroes first meet, they fight for a bit, all for the express purpose of... well, not overwhelming one another. No one is hurt. It's just a way to break the ice, as it were. We also learn that the mysical, spell-encrusted hammer of a literal god cannot smash through a sliver of metal.
The Hulk vs. The Abomination in 'The Incredible Hulk'
What would happen if The Hulk fought an equally powerful iteration of himself? A lot of punching, it turns out. And punching that doesn't hurt, bruise, or even remotely phase the other. Ultimately The Hulk strangled The Abomination to death with a chain. Next time, Hulk, lead with that. Keep garrotte wire handy.
Wolverine vs. Deathstrike in 'X2: X-Men United'
One would think having razor-sharp knives hidden in your hands would be a great way to do damage, and that watching two such people knife-fight would be a bloody affair. Wolverine and Deathstrike, however, both have a super-healing superpower that undoes any damage almost instantly. Sure, it hurts when they get stabbed, but they heal so quickly, stabbing does little to slow them down. Ultimately, Wolverine injects Deathstrike with liquid metal and drowns her in water.
Image: 20th Century Fox
Thor vs. Anyone, Really
In Thor: The Dark World, Odin, the king of the Norse gods has a baffling line of dialogue. He says something along the lines of "We are not gods, and we can die." Only that's wrong. You guys are gods. You look and act like gods and you're largely indestructible. Call a spade a spade. Of course, if they did that, then they'd have to admit that going into battle against Thor is a churlish exercise for everyone. He's essentially immortal and indestructible. If he can be hurt, it would be nice to know what can actually hurt him. After 13 films in this series, we still don't know. In all of his fights, he's come out unscathed. Why would punching him do anything to him? All it's done - as seen in all his movies - is get him to break into a healthy sweat.
Superman vs. Zod in 'Man of Steel'
The superhero fight to end all superhero fights depicted Superman - invulnerable - punching General Zod - also invulnerable - across the sky. They punched each other through buildings. They punched each other into the ground. Nothing happened to either of them. At the end of the day, Superman broke Zod's neck. He didn't try to keep Zod away from the ground or take him to the moon or anything. He just punched and punched. The punches don't hurt anymore. Either take him away from Earth, or lead with the broken-neck thing.
Image: Warner Bros.