I have a strangeness when it comes to birthdays.
I'm really good at remembering people's birthdays, though I rarely do anything special other than say happy birthday to them, unless no one has done anything for them, at which point I usually try to make up for everyone else's inconsiderateness by summoning up some close friends for dinner or hanging out someplace.
At the same time, I ignore and downplay my own birthday, and prefer that a big fuss isn't made about it... but if the people who are close to me don't remember it I feel hurt... as if they should remember it because I remember theirs. I'm not expecting gifts of any kind, and would probably crawl under a bed and hide if someone threw me a party... but it's really nice to know I'm cared about enough to acknowledge that someone remembered what day my birthday was.
However, I patently refuse to tell people how old I am, unless forced, and I don't know why other than I prefer to avoid arbitrary labels when the connotation doesn't apply to me. It's like telling people my age is lying to them about who I am because of the expectations associated with it. But, I think this issue is less related to birthdays than my need for being true to myself (my strong Fi and Fe mix), as it applies to a few other things such as "Where are you from?" or "What religion are you?"