Well let's look at this logically by analyzing their attacks and resistances. For the purposes of this discussion, I am neglecting "other", as this would seriously complicate the comparisons. In addition, I must ignore power ups and upgraded abilities, otherwise things like Mario's Invincibility Star or Megaman's potential invulnerability with the Rolling Shield (from Megaman X) make the answer trivial and/or nonsensical.
So without further ado, let me first eliminate the individuals that possess little chance in this brawl...
Bowser
Because Bowser has a glaring weakness, he is the easiest to eliminate in this battle. Bowser possesses a chronic weakness to Mario, which just happens to be another combatant on this list. As such, Bowser is easily eliminated in this battle.
Simon Belmont
Simon's primary attack is a whip. Though effective against undead and damaged castle walls, I can't imagine his attacks would be too effective against the other combatants, especially the armored duo. Aside from jumping, he possess no other defenses. As such, I must rule out Simon Belmont.
Mega Man
Megaman possesses the means to use a distance attack via his Buster Cannon. However, Megaman possesses a distinct disadvantage: in very few of his games can he fire in an upwards direction. This gives him a distinct disadvantage against combatants that can jump and get above Megaman, which unfortunately is the all of the combatants except Link. (Yes even Bowser jumps, recall boss fight in SMB3 and the second Bowser fight in SM64).
The last three oddly enough form a sort of rock, paper, scissors combination. Let me elaborate.
Mario beats Samus
Mario's strength is his jumping ability. Like Link and Belmont, Mario is a close range fighter that would typically be at a disadvantage to Samus. Mario, however, possesses a distinct advantage: a superlative dodging ability. He's dodged a variety of attacks including both bullets (recall Bullet Bills) and blasts of energy (fire balls from piranha plants and magi-koopas). As such, despite Samus's amazing offense, Mario endures like the rabid jumping cockroach that he is. Samus would fall in this pairing.
Samus beats Link
In this unfortunate pairing, Link is bringing a sword to a gun fight. Even if Link possesses a basic Hylean Shield that he sometimes obtains at the outset of game (as in Windwaker), please keep in mind the caliber of weaponry of his opponent. Samus is using advanced chozo weaponry, effective against even armored space pirates that would possess much better defense than a simple soldier's shield. With flimsy defense and only close range attack capabilities, Link would be destroyed.
Link beats Mario
Mario's weakness: things with spikes on their heads. If Link just holds his sword over his head like a single giant spike, Mario can't do a single thing to Link. Using only game mechanics, if you'd like, Link can spam his overhead slice technique (seen in any of the 3-D Zelda games) and Mario still can't touch him. As Mario possesses no defense against stabs and slashes, this battle will ultimately fall in Link's favor.
So now we are left with a unsatisfying three way tie. To dissolve this stalemate, we must consider if one of these three individuals might meet an earlier demise. The key here is Megaman. Megaman, like Samus, possesses advanced weaponry capable of penetrating Link's primitive shield. As such, between both Samus and Megaman, Link is likely to meet an untimely demise while both Mario and Samus would make it to the final rounds of this battle.
And so we have a winner.
Mario wins
Otherwise he's dead too.
