He's mean, he's green, and he's possibly the most brutally powerful comic book character ever made.
The Incredible Hulk was created in 1962 by the Marvel tag-team of Stan Lee and Jack Kirby. Comic books wherein superheroes would battle a monstrous freak of the week were common fare. For a twist, they created a character who is still a savage engine of destruction but not necessarily the bad guy. Plus they could have him fight the army and other superheroes with the defense that Banner isn't generally in control when someone gets the Hulk's dander up and sends him on another rampage.
The Hulk is one of comics' bar-setting characters. Just as a character's intelligence may be refrenced in comparison to Batman or his speed as compared to the Flash, characters noted for their strength have to measure themselves against whether or not they could survive a brawl with the Hulk.
Once the Hulk gets started on a gamma-fueled bender it's quite difficult to get him to stop. This is because as his anger rises so does his strength. This usually leads to the destruction of entire city blocks (or entire cities), which results in some superhero team or another trying to corral him, which of course gets him even angrier and stronger. He's moved mountains, smashed countless robots, and even broken supposedly-unbreakable adamantium (courtesy of Wolverine's spine).
Not only does Hulk regularly destroy everything within a few miles of him, but he's ridiculously difficult to put down. He has survived bullets, bombs, nuclear blasts, planet-cracking explosions, and has traded blows with the strongest characters in Marvel and elsewhere. He's also been known to spontaneously develop amphibious lungs, absorb magic to get stronger for some reason, and on at least one occasion Banner attempted to shoot himself to end the Hulk's existance but hulked out before the bullet could kill him. In other words, the Hulk is immune to damn near everything and is strong enough to break just about anything.
Most superheroes fight each other on a regular basis anyway, but when you're the biggest and the strongest like the Hulk you have a particular duty to pound the faces of as many folks as you can find on a regular basis. Naturally the most crowd-pleasing battles are against similarly powerful opponents.
Though an off-and-on member of the team himself, the Avengers have been called in on several occasions to try to stop the Hulk's rampage. This usually means Hulk will be going toe to toe with the mighty Thor, one of the team's strongest bruisers (next to the big green guy himself). The hammer-wielding superhero was in fact created as something to surpass the Hulk, as when you've made the strongest human or metahuman you can, the next step up is something that's not human. Flight, super-strength, centuries of combat experience, and a host of other storm-themed powers make him a good challenge for the Hulk.
Their first clash in the '60s actually led to the formation of the Avengers, and the two would meet in battle many more times over the years. Few powerhouses can trade blows like Hulk and Thor, but the Hulk came out on top more often than not. Hulk is also one of the few to have successfully lifted Thor's hammer Mjolnir, supposedly impossible for anyone but Thor. (Impossible as defined by comic books, anyway.)
Iron Man's combination of powered armor and technological ingenuity make him an effective and adaptable fighter. In addition to combat training from Captain America himself, Iron Man often modifies his suits in the midst of a fight to meet a new threat and has numerous variant suits for special purposes. None among these is designed for such a specific situation, however, as the Hulkbuster armor, crafted for the sole purpose of surviving a scrap with the Hulk.
We say 'surviving' rather than 'winning', because it appears that even the best tech can't do more than slow the Hulk down. In early battles before the Hulkbuster armor, Iron Man would often go down with just a few hits as the critical damage to his armor endangered his heart condition. In 1980 Iron Man did manage to serve the Hulk a knock-out and very nearly finished him off, but again the armor couldn't take any more stress.
On one hand Iron Man deserves some props for showing the commitment to coming back for another round even though Hulk nearly kills him almost every time. On the other hand Iron Man had the idea to launch Hulk into space to keep him from destroying a city every other tuesday, leading to Hulk eventually coming back and tearing up the planet in his most destructive rampage in Marvel comics history, so maybe old shellhead deserves a few hard knocks.
The last son of Krypton holds the same throne in DC Comics as Hulk does in Marvel, his strength and stamina seemingly limited only by how far he pushes himself, making a cross-brand confrontation between the two inevitable. Superman is known for performing some rather ludicrous displays of raw power, moving entire planets and causing sonic booms from the force of his punches when he goes all out.
There were a number of one-off DC vs Marvel issues in the 80's, and Superman first met the Hulk in battle as part of a team-up with Spider-Man. The two would have their first stand-alone duel in '99. The Hulk wins their first showdown, and second later in the issue is more or less a draw as Superman throws Hulk at one of Lex Luthor's gadgets to smash it.
The biggest throwdown between these titans would come in '96, in the Marvel vs DC crossover series that pitted numerous characters from both franchises against each other, several matches calling for fans to vote on the victor. By popular demand, when Superman and Hulk slugged it out again the man of steel emerged victorious. In their one-on-one battles this puts Hulk and Superman tied with one win apiece.
Competing for the role of 'powerhouse with an oft used catchphrase', the Thing of the Fantastic Four has a long-running rivalry with the Hulk and has gone toe to toe with him dozens of times. His ever-increasing strength and durable rock-like skin allow him to match the Hulk blow for blow, and he has the added bonus of military and martial arts combat experience. In addition, while Hulk's intelligence and coherance are put on a back burner when he unlocks his fury for greater strength, Thing can keep his head in the game.
Thing is a member of the highly-exclusive club of folks able to make Hulk stay down for the ten-count, beating him badly enough to get him to pass out and revert back to Banner, though in a majority of their battles the Hulk appears to have the advantage. This seems to have given Thing a bit of an inferiority complex, given how often he picks a fight with the Hulk just to have another round.
However, perhaps to intentionally keep the rivalry going, Thing and Hulk rarely get a chance to carry the fight to the end. Either someone intervenes or one or the other of them is taken out of the fight. When the Hulk decides he doesn't feel like fighting anymore he's been known to bury the Thing in concrete, drive him into the ground like a nail, or simply knock him out of the park.
The two continue to compete, sometimes in genuine combat, sometimes in staged sparring matches for charity and/or the amusement of alien overlords, and sometimes just anything they can find in which to go head-to-head.
And we do mean anything.