Learn English – What’s the word for someone who doesn’t appreciate what he has and wants more

How about favoured (or favored if you're American)? To me that implies that you've received a lot, without specifying money, and also without implying either way whether you're deserving or not.

Consider the term aficionado (“A person who likes, knows about, and appreciates a particular interest or activity; a fan or devotee”), for use in a phrase like “She's an aficionado of life.” I don't know of an adjectival form.

The verb savor (“to appreciate, enjoy or relish something”) is relevant, eg “She savors life.” Again, I don't know of an adjectival form.

The adjective appreciative (“Showing appreciation or gratitude”) may apply, but is somewhat nondescript and general. Optimistic, positive, and upbeat (“Having a positive, lively, or perky tone, attitude, etc.”), are perhaps more relevant; a sentence like “Sally's an upbeat person” implies Sally is an active person, appreciative of life, has positive attitude, etc.

The adjectives epicurean (“pursuing pleasure, especially in reference to food or comfort”) and hedonistic (“Devoted to pleasure; epicurean”) may apply but are slightly pejorative. (Note, hedonistic is antonymic to ascetic (“...characterized by rigorous self-denial or self-discipline; austere; abstinent; involving a withholding of physical pleasure”).)