If I summon a world breaker can I exile a card my opponent owns?
Worldbreaker's cast trigger says:


  When you cast World Breaker, exile target artifact, enchantment, or land.


So, when you cast World Breaker, you pick a target.  It doesn't have to be one of your artifacts, enchantments or lands.  

However, for the return ability:


  {2}{C}, Sacrifice a land: Return World Breaker from your graveyard to your hand.


Using that ability would require you to sacrifice one of your own lands (which means putting that land into the graveyard; it won't get exiled).  You can't sacrifice something you don't control (although if you somehow came to control an opponent's land, you could sacrifice it even though you don't own it).