We define successful aging as maximizing your potential and minimizing the negative effects of getting older (such as the weakening of physical and mental abilities).
Genetics is certainly one key to successful aging. If your parents and grandparents lived long and healthy lives, the odds are you can expect the same.
But, there's a lot more to aging successfully than just genetics. Eating right and exercising, making sure you get regular check-ups and screenings, and focusing on preventive care are very important to how well you age.