We have always celebrated our cat's birthday in my family, yes. There's usually a special meal (well, just her favorite wet food most of the time) and my daughter always has to give a present or two.
Then we have the annual photography session to get the birthday picture taken. I guess it boils down to a day of spoiling for a cat who's already pretty much spoiled to the max. :-) But I'm so glad we have all those birthday pictures. That cat's been through a lot for those pictures because my daughter always has to fancy her up... birthday hat, beads, etc. Most of the kitty faces on the birthday pictures look very annoyed. hehe
I like the idea of celebrating the day the pet came into the family if you don't know the actual date of birth!