Age matters. How much it matters depends on your lifetime goals. Do you want to simply have fun and make music for yourself or family? Perhaps you have greater aspirations. In the latter, age matters very much. The window of greatest opportunity begins to open at about the age of two, is fully open between the ages of seven and fifteen and is nearly closed by age twenty-five, this window is never fully shut, however.
Is there a best age to begin?
Here's my personal experience.
I learned to read music when I was 7 (I played the trumpet and the recorder for a couple years, just kid's stuff). Until the age of 13, I simply lacked the desire to learn piano. Now, 14 years later, I've learned 29 Beethoven Sonatas, most of Mozart's Sonatas and about half of what Chopin wrote, lots of Bach too, only recently adding piano concertos to my repertoire. At the age of 27, I'm improving very rapidly, both technically and artistically. This success came at a price; a nine year period of seemingly endless work and gradual improvement. All of a sudden, at age 22, I began to improve by leaps and bounds. Patience had carried me through.
Had I started at the age of seven, I believe I would have reached my current level at around 18 and with less work. Had I started at a later age, I would have reached my current level at a later age. A pianist's full potential can only sometimes be realized starting at a late age. This thought mustn't dominate the beginner's mind. Dwelling on unchangeable factors (like age or height) is the most destructive thing a pianist can do. Your main task is to identify and correct the problems that can be changed. (A good teacher is indispensible, here!)
The artist who starts late, should be very careful not to confuse artistry with virtuosity. Artistry is the goal, or (unfortunately) in many cases, it should be. If your neophyte technique prevents you from playing a certain piece, pick an easier one. Don't overreach. Just move at your own pace, trust your teachers and have faith in yourself. The only thing that needs to be done, is the next step. Be realistic, don't assign limits to your potential and most of all, have fun!
The piano will give joy to anyone who enjoys it.