Covet, envy, grudge, begrudge though not closely synonymous all carry the implication of a selfish desire to have something for one’s own enjoyment or possession.
To covet (for fuller treatment see DESIRE) is to long inordinately for something which belongs to another.
To envy is to regard another with more or less chagrin, repining, jealousy, or hatred because he possesses something one covets or feels should have come to oneself.
To grudge orbegrudge implies reluctance or hesitation (often through selfishness, meanness, or stinginess) in giving another what he (or it) ought to have because it is his (or its) due or need.