Besides the usual advice on staying young such as eating healthy and keeping active, one of the biggest reasons people start feeling their "age" is due to limited mobility. Having trouble reaching for things from the floor, getting up off the floor or a chair, pain from prolonged activities such as walking or standing, and sense of imbalance and a hyper-alertness to potential falls are all things that make people feel old. A gradual loss of independence is a slippery slope when nothing is done to slow the aging process.
Finding ways to maintain your agility is highlighted in Frank Wildman's book "Change Your Age". Solidly grounded in the Feldenkrais Method  of movement education, short, sensible lessons are provided to help people feel and move younger.