Amy is a member of the family Wong. The Wongs are extremely rich, as they bought the entire western hemisphere of Mars by trading a giant diamond to the native peoples. They also claim it is easier to brand everything that isn't their's, since they own so much. Amy doesn't dress the part of a rich girl because she likes the idea of having her own identity.
Amy attends Mars University, which is partially owned by her parents. She went to a class with Fry once, but Fry dropped out. She is studying in engineering and she is an intern at Planet Express. She is capable of piloting the ship, but has not done more than once.
Amy is mostly concerned with her looks, as she thinks she is quite possibly the cutest girl out there. She was apparently so cute, she had to have cuteness reduction surgery. As a child, she was extremely obese, and her dad often made fat jokes. She often competes with Leela in looks and love life. She has several tattoos, including a talking devil, horse, and a blurred one (supposedly modern TVs don't have high enough resolution to view it). Although she has these tattoos, they never stay, and disappear in the next episode.
Once in a car accident, Amy had Fry's head attached to her shoulder to keep him alive. She was dating Fry at the time, and they soon broke up. Amy has then proceeded to date many men on the show, and her only long-time relationship was with Kif Kroker, who became pregnant with Amy. (Kif's people have 'smizmars' which are the inspiration to have children. Leela was technically the mother, because it only takes a touch skin to skin for Kif to become pregnant. Amy was still considered the mother.)
Amy is not the smartest girl and is a major klutz. She slips on practically anything and falls off more things than most people. She often makes comments about Leela's appearance that tend to have a subtle harshness to them and doesn't ever seem to realize she's done any wrong.