Who would win in a fight between Superman and the Hulk?

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Ordinarily I would call this fight for Superman as eventually he would realize that Hulk just gets more powerful the more angry he gets and back off until he calms down. That is the only rational way to beat the Hulk under normal circumstances. You defeat his anger.

According to DC's pre-crisis canon Superman has incredible power for a Kryptonian. Superman is so powerful that in order to properly function he has to put in place mental blocks or limiters to his strength so that he is not a danger to everyone around him.

According to Marvel canon Hulk has nearly limitless power equal to or exceeding his anger. He gets more angry the more he is hurt and when he is losing. Hulk can recover from almost any injury which again makes him angrier.

Skip to the end for the summary.

Superman Breakdown

Strength: Can lift or manipulate between 66 quintillion and 400 quintillion tons.

• Has moved the Earth around before (66 Quintillion tons)
• After being supercharged by the sun, he was quoted as being able to lift 200 quintillion tons with just one arm and stated he thinks he could lift much more. We should give him the benefit of the doubt and say with both arms he should be able to lift 400 quintillion tons.
• Can do the Infinite Mass Punch which is a punch at or near the speed of light causing the punch to impact with near infinite mass.

Durability: Superman has survived numerous attacks in the past that are quoted as being of equal power to a supernova and has experienced some even more powerful attacks.

• Can take a 10 octillion megaton yield of a relatively small supernova blast without being supercharged by the sun.

Speed: Superman is capable of Faster Than Light travel and can bend space-time around himself to go even faster. He can even go so fast he can leave our universe if he unleashes all of his barriers.

• Batman has stated that Superman's fastest recorded speed is 10,563,300,000 mph (10.5 billion mph). That's 15.75 times the speed of light.
• He has been compared in speed to the Flash when Superman is going his fastest and Flash is not overexerting himself.
• Batman also says that Superman can perceive things happening with Zeptosecond precision. That is one sextillionth of a second.

Weaknesses (Not including depowering ones):

• Respect for life.
• High moral standard.
• Must remove self imposed limiters and blocks sequentially to access his full power.

Superman reference: Final Analysis for Superman and Goku (w/ power levels)

Hulk Breakdown

Strength: Effectively limitless depending upon his emotional state. "The madder Hulk gets, the stronger Hulk gets." Starts out at roughly 100 tons of lifting capacity.

• After some probing, the entity Beyonder once claimed that the Hulk's potential strength had "no finite element inside." — "Betrayal!" Secret Wars II 8 (February 1986)
• The Hulk is also able to generate omnidirectional bursts of kinetic energy that can completely destroy the planet he is standing on. — Incredible Hulks #634-635 (2011)
  
• He can grow stronger from radiation. — "Planet Hulk Armageddon Part II" The Incredible Hulk v3, 105 (June 2007)

Durability: Hulks body will mutate as needed to compensate for any external threat including crushing pressure underwater, the surface of the sun and outer space as long as he stays mad.

• "Cold Storage" The Incredible Hulk v2, 394 (June 1992)
  
• Has withstood the equivalent of solar temperatures. — "Sins of the Father" The Incredible Hulk '97 1 (1997) | "Hulk" World War Hulk 2 (September 2007)
  
• Has survived attacks that can shatter a planet. — "Kids Will Be Kids" Marvel Comics Presents 52 (June 1990) | "Heart of the Beast" Silver Surfer v3, 125 (February 1997)
• Can survive outer space. — "Casus Belli" World War Hulk Prologue: World Breaker 1 (July 2007) | The Incredible Hulk #90, Nick Fury states that Hulk's mutations can alter his body to adapt to space.

Speed: Hulk is capable of Superhuman speeds of several hundred miles per hour and can enter low Earth orbit through jumping. He can then also survive the re-entry from low orbit.

Weaknesses (Not including depowering ones):

• Dumb as a box of rocks.
• Will lash out in rage without thinking through his actions.
• Starts out at 100 tons lifting strength and only increases in strength proportional to his anger.

FIGHT!

I think I have to give this fight to Superman with one caveat. Superman would do everything he could to not kill the Hulk. Superman is faster and smarter and has a wide range of utility abilities at his disposal that Hulk cannot compare to. Hulk has no limit to his strength and is effectively immortal so long as he remains angry. Unfortunately Hulk also starts off much weaker and cannot easily increase his strength on demand.

This is how I see the fight playing out.

Hulk likely starts this fight with a good punch to Superman which he shrugs off as pictured above. Superman ever the reasonable one, tries to talk Hulk down but this only makes Hulk angrier and results in stronger punches. Superman might start out with a few blows to test the Hulk's strength making Hulk very mad at the "Little blue man". Hulk would lash out at him in return. Superman would then realize he needs to cut out some limits and ramp up in strength. Hulk would get angrier because he is "Strongest there is!" and match Superman.

Eventually Superman would move the fight to another planet possibly one of Jupiter's moons as he did in Superman vs The Elites. He doesn't want innocents to be harmed in the coming fight. He might take some serious blows from Hulk while trying to drag and throw him to IO. Superman would then leave IO and do an extended sundive to power-up. While he is performing his sundive he would be cutting out his limits like he normally would to prepare for interstellar travel.

Hulk would get very angry at being left there alone "Hey! This fight not OVER!" and jump off towards the sun. Strong as he is he might be moving pretty fast but nowhere near Superman's speed. At this rate it might take Hulk a while to get back to Supes.

The now overpowered and unlimited Superman would fly back toward IO at near light speed and do an Infinite Mass Punch on the Hulk that is now hurling through space.

With Zeptosecond precision, Superman would break off his attack at the exact moment when Hulk is about to be killed. He would then throw the unconscious Hulk somewhere on Earth that is deserted and pleasant to rest.

Hulk can be overcome if he is attacked with a sufficiently strong attack to beat his resistances before he gets too angry to shrug off the attack. Superman on the other hand can willingly remove all of his barriers and boost himself with solar energy at will. This lets Superman ramp up his power faster than Hulk can boost his anger effectively beating Hulks resistance to damage. The Hulk on the other hand for all of his strength just isn't fast enough to even hit Superman easily.

Just for reference, all three times they have actually fought in the combined Marvel / DC comics Superman has won.