Something I've noticed whilst I'm learning Italian is that when you have a phrase such as "ti chiamo" is that the the action described is being applied to the subject of the sentence, and the conjugation determines who is performing the action ("I call you" in this instance). 

However, mi piace (or even mi piacciono) seems to be an exception to this, as it means "I like". My question is whether this reversal is rare or I just haven't come across examples where this structure is used.