In 2002, FIDE added birthdays to the data kept for FIDE-rated players. The world federation distributed birthday data for four years, then started broadcasting birthyears only. The following table shows the number of rated players listed with their birthday. (For an explanation of the big jump in number of players from 2002 to 2003, see Inactive Players Missing.)
The percentage of players listed with a birthday is higher than I expected. I was also surprised to find my own name listed with a birthday. At the time the field was incorporated into the data, I hadn't played a FIDE event for over 10 years, and couldn't remember ever giving my birthday when registering for a tournament. I obviously did, and FIDE must have retained the data until ready to use it.