Well, here's a more sane, albeit less imaginative, answer :)
If Mario didn't die during the fight, as would usually happen in a mario game, he would most likely be placed in the dungeon. Princess Toadstool would be forced to marry Bowser and the Koopa King would eventually take over the Mushroom Kingdom. A Mushroom rebellion would ensue but all their efforts would be dashed with one good zap of a magic wand. And Mario, of course, will try beyond hope to escape and defeat Bowser once more, although he'd be in for a much tougher fight.
Over time, Peach would probably discover more about her husband, such as how the Koopa Kids came into being and even what happened to her mother. (it's sad really) And once all opposition has been crushed on the Mushroom World, a disillusioned Bowser would probably ask Kamek to seek out new worlds for him to conquer, like maybe Earth or Moebius, worthy challenges for the mighty Koopa King.
But that's just my theory.
I'm sure someone can come up with a better one. :)
Signed,
Warewolf at Large