As several members already posted, it is more about health than age. I certified in December '09 at age 63, after clearing it with my doctor. The certification dives for OW were all shore dives at La Jolla Shores, and were doable, though difficult for me. My AOW dives took place at LJS (2) and Catalina's Casino Point Marine Park (3).
I am now a big fan of diving that does not require the considerable effort of a long walk wearing all my gear, an entrance through the surf and a long surface swim, all before beginning the dive, then repeating the journey in reverse after the dive. This means I am diving from boats and at Casino Point. I tried a La Jolla Shores dive on Sunday and although I completed the dive, I will probably not be going back anytime soon. For me, it is too much effort for too little bottom time.
The obvious drawback to boat diving is the price, but I belong to Power Scuba, and Bill Powers negotiates some sweet prices for the group from local dive operators. I can afford to go on two or three trips a month, 2 and 3 tank dives, so I get in six or eight dives a month at some really great sites.
I think any healthy person can learn to dive under the appropriate conditions, regardless of age. My wife is considering learning to dive, but if she decides to do so, will do it from boats or at Catalina. This is after watching me get my rear end kicked at LJS the other day.
My $.02.