Maybe it motivates you, but an even better method is trying to be better than yourself. How about pushing yourself each day to eat better or to walk longer after dinner? Goal setting is a great way to compete against yourself. You select the end result that you want and then it's up to you--and only you--to work for those goals. You'll be pushing yourself toward greatness, not creating unnecessary competition against others who can't compare to you
I have to concur, though I was very competitive when I was younger, my wife and kids are all non-competitive. But they do believe in their own physical health. They all have their own routines at home, including use of an indoor stationary bike and treadmill as well as regular family walks outside. Non of us are interested in going to the Gym or competing with others to attain physical health.