The purpose of this study is to assess the safety and the body's immune response (body's defense against disease) to an experimental H1N1 influenza vaccine. Up to 650 healthy volunteers from three age groups (greater than or equal to 6 months to less than 36 months, greater than or equal to 36 months to 9 years, and 10 - 17 years) with no history of influenza H1N1 2009 influenza infection or influenza H1N1 2009 vaccination will participate. Participants will be randomly (by chance) assigned to 1 of 2 possible H1N1 vaccine groups. Group 1 will receive 15 mcg of vaccine; Group 2 will receive 30 mcg of vaccine. Participants will receive vaccine injections on Days 0 and 21 in the arm or thigh muscle. Study procedures include: medical history, physical exam, maintaining a memory aid, and blood sample collection. Participants will be involved in study related procedures for approximately 7 months.