I think you become old at the point you accept the label :). I know some people who are hobbling around and contemplating the end of their life in their mid-60s....then on the other end of the spectrum, I recall a woman who stopped to talk to me while I was working at Wal-Mart some years ago. She was visibly an older woman, but in surprisingly good health and very active for what I judged to be her 70-some-odd years. We chatted about the horses she was to start training that spring, and about the trails she'd enjoyed snowshoeing on the month before....and in the middle of all this, she exclaimed, "And I'm 97 years old!!"
I'm 25 -- at the time I was 19 or 20 -- and in that moment, 97 didn't seem so old. That same week, a 67-year-old co-worker died. By his activity level and outward demeanor, I would have never guessed he was so young. Now I'm married to a 52-year-old who is convinced he's old, and I'm having a heck of a time explaining to him how no one is truly old when he can still curl up in front of a kung-fu movie with the 5-year-old and both of them giggle about the main character not getting a kiss from the leading lady.