Mine, no (I couldn't even if I wanted, it's on a day a bit hard to fail to notice it).
I don't remember anybody else's birthday, however I have notices on my cell for a handful of people taht I know they'd like my remembering their birthdays. Not that it helps very much, since I don't exactly watch my mobile all the time, but it's better than nothing.
It's my mother's birthday today... it didn't immediately pop up in my mind... until I was reminded of the date. I have difficulty tracking dates... compounding on my inability to recall exact names and numbers... no surprise that I am bad at recalling birthdays.
The only way I would remember it is if I have something planned specifically for that day. Otherwise no...
I'm inclined to forget my own birthday but on my birthday, the second of April, our local busker sang me happy birthday with his guitar. And when I went to the doctor for a check-up, the staff all sang me happy birthday.
So they just won't let me forget. Still it was very nice.