If someone can't be satisfied, she is insatiable. After being lost in the woods eating only berries for a few days, you'll find your hunger is insatiable once you finally get to the table.
Insatiable comes from the combination of the negative prefix, in- and the Latin verb satiare, for fill. Someone who is insatiable can never be full. It can be used for spiritual as well as physical desires. Swift's traveling Gulliver talks about his "insatiable desire of seeing foreign countries." Perhaps you have an insatiable desire to learn all the words in the English language. Synonyms are unappeasable and gluttonous.