Everyone can benefit from stretching, young or old. Flexibility prevents injury because you have a full range of motion available for normal activities. If you add stretches to the end of an exercise program it may also help to decrease muscle soreness. Even the connective tissues such as the tendons become more pliable and resilient. An exercise program which includes stretching will improve muscle tone and condition the tendons that hold them to prevent injuries.
My most dedicated student turned out to be a concert violinist named Gretchen who complained of ganglion cysts in her wrists when she joined my flexibility class for adults. Playing the violin did not require supple wrists so long as her fingers were able to press the strings that needed to be played. However, Gretchen was looking for something that would improve her ability and pull her out of a playing rut she fell into the past few years. Gretchen was 45 years old when she joined my flexibility class for adults and her attendance lasted four consecutive years.
As Gretchen progressed over time she began to exclaim that her ganglion cysts were shrinking and the wrist stretches in my class were helping her to play the violin better. At the end of the first year Gretchen discovered how much room for improvement her stretching had overcome. Not only was she playing the violin better but everything about her had improved. She was more fit, had more energy, felt young and supple, and her confidence was at an all time high.
It is in our nature to stretch. When we yawn and extend our arms to stretch it feels good. We can capitalize on this natural habit and develop a program which accents our built in nature to stretch. Give your body what it calls on you to do natually. Stretch. It makes you feel good. 
