Think about it - assigning an extra number to your age for every year you are alive doesn't make as much sense as it should. The difference between a 65 year old and a 75 year old is less than between a 20 and 30 year old, which is less than between an 8 and an 18 year old. Ten years of age means different things at different stages in your life.
I propose an alternative: they need a name, but for now I will call them cycles. Cycles will be based on powers of phi, or 1.618... The first cycle ends at, approximately, 1.618 years of age. The second cycle ends at 2.618 years of age.
The third, 4.236 years of age.
The fourth, 6.854 years of age
The fifth, 11.090 years of age
The sixth, 17.944 years of age
The seventh, 29.034 years of age
The eighth, 46.979 years of age
The ninth, 76.013 years of age
The tenth, 122.992 years of age.
This is a nice system. For one thing phi, or the Golden Ratio, is nice. Secondly, these cycles cover the fundamental epochs of a person's life - 18 is the age of majority in many countries, 11 marks the onset of puberty, and everything changes when you hit 29 . Thirdly, no one is likely to make it past 10 cycles, which makes it nicely compatible with our base 10 civilisation.
(Birthdays would still be celebrated - but with this, you get extra holidays! Happy Start of Seventh Cycle!*)
*Since I came up with this years ago - I actually celebrated this. Privately, of course