CrossFit puts a lot of emphasis on the importance of the squat. The push-up is another thing that, like the squat, can help keep you out of the nursing home. The NYT article linked below notes that "People who can’t do a push-up may not be able to help themselves up if they do fall.
"Based on national averages, a 40-year-old woman should be able to do 16 push-ups and a man the same age should be able to do 27."
At CrossFit Seattle we love to show men and women who say they can't do any push-ups several ways to start doing them--and they succeed.
Jack LaLanne, reportedly still working out with push-ups, says he does them with hands and feet elevated so he can "go way down, even lower than if I was on the floor,” he said. “That’s really tough.” REALLY TOUGH, but he does them. A lot of exercises are never going to be easy, but that's irrelevant to their value. Do them anyway and you'll be glad you did.
"If the floor-based push-up is too difficult, start by leaning against a countertop at a 45-degree angle and pressing up and down. Eventually move to stairs and then the floor."
"An Enduring Measure of Fitness: The Simple Push-Up" in today's New York Times online blog "Well."