The Whomp King is, as his name suggests, the king of all the Whomps in the series. In both his 3D Mario appearances, he is seen guarding a Power Star in Super Mario 64 and Super Mario Galaxy 2 respectively.
In Super Mario 64 Edit
Like most of the other bosses in the game, the Whomp King precedes his fight with a speech explaining how his kind gets walked over all the time: the humans need to get taught some respect!
His main attack is to jump and try to crush his opponent. This reveals his weak spot (the Ground Pound emblem on his back). After being ground pounded three times, the Whomp King explodes and the Power Star can be retrieved. In the remake of Mario 64, the Whomp King now wears a golden crown so he can be distinguished from the other Whomps.
In Super Mario Galaxy 2 Edit
Both the Whomp King's speech and fight is nearly identical to that of its 64 appearance. This is fitting, too, because he appears in the Throwback Galaxy level. If the player dies during the fight, the Whomp King will say he's tired of his speech and simply begin the fight.
Whenever the Whomp King ground pounds, he now creates a shockwave which will make Mario paralyzed if he doesn't jump at the right time. He can also create miniature Whomps called Whimps that chase after the player during the fight.