Of course. My dad's neighbor still competes at age 75. Many races have categories for masters and seniors. Here's a couple books to get you started:
Author Friel, Joe.
Title Cycling past 50
Publisher Champaign, IL : Human Kinetics, c1998.
Author Sloan, Jim, 1956-
Title Staying fit over fifty : conditioning for outdoor activities.
Publisher Seattle, WA : Mountaineers, 1999.
Edition 1st ed.
Author Overton, Ted, 1920-
Title Sports after 50 : fit yourself into fun sports
Publisher Annapolis, Md. : Azimuth Press, c1988.