I keep 14 clubs, a dozen balls, two towels, and a thermos of coffee in my bag. I carry it with no problems. I've been carrying my clubs since I was 11, and not sure that I'd know any other way to do it. I had to take a year off from walking in 2010 due to a really bad ankle injury that lead to some foot problems, but never any shoulder or back problems.
I do ride a lot of rounds, such as when I play a resort course where the cart fee is included, with friends who insist on riding, or when I'm playing with my drinking buddies. I probably walk 2/3 of my rounds.
I have a buddy, 37-yo, who has a push cart. He's in as good or better shape than me. I break his balls about the push cart, but that's just guys being guys--I don't care how he gets his clubs around the course.
Interesting factoid: I was visiting this buddy in Dallas a month ago, and we decided to go play golf at a semi-private club. It was cold, so we were definitely going to walk. The club would not let him use his push cart--the marshall stopped us on the range and said if he was going to use a hand cart, he had to rent one from the club.