Of course Elton John has written many songs, as has Bob Dylan, both since the 1960s.
Neil Sedaka has been writing songs since the 1950s, and still is.
http://en.wikipedia.org/wiki/Neil_Sedaka
Pete Townsend has written for the Who since the 1960s.
The Bee Gees have been writing songs for themselves and others for years (since the 1960s)
There are loads.
In fact any writer who has been writing songs since the 1950s or 1960s (and still is) could be the writer of the most songs.