32 Mushroom Conspiracy.

OK, from the Mario RPG series, it’s become common knowledge that Bowser at least has feelings for Peach (as stated in above comic, human females are considered the most attractive universally, so it’s not far-fetched). In Super Mario Bros, he kidnaps the princess for his own pleasure and then leaves his forces to patrol the area. He basically hosts a hostile takeover to add more land (Mushroom Kingdom) under his rule. To enforce his rule, he built castles deep into the heart of these lands from which to rule over. After initially failing to govern each castle in rotations, he would assign various leaders to the territories (brainwashed kings from the lands before Bowser, his own children, vicious monsters, etc).

I think its more of a quest for power than a quest for Peach, but his soft side can’t bring himself to kill her, so Bowser captures her before each takeover. Later on his motives might change- for example, his takeover of Dinosaur Land (Super Mario Bros World) was probably just him ticked off after losing to Mario so many times (he apparently crash landed there, as evidenced by the airship next to Bowser’s cave in the water). Plus, the more times Mario thwarts him the more likely it is each kidnap is a ploy to crush Mario.