How interesting. I did that recently (removed my birthday) and thus didn't get as many greetings as I did in the past when my birthday came up. Those who remembered were mostly friends and family whom I usually greet anyway. There were a few who copied others just for the heck of it. But I went ahead and thanked the ones who did say happy birthday to me.
Personally, I couldn't care less if others greeted me or not, but it's the others I get conscious of greeting.
I honestly don't care much either way either, I just like doing mini social experiments using Facebook I guess.

My real answer to your original question is that it really doesn't matter that much. Maybe if there is someone close to you who like you or me took their birthday off their profile, I would try to remember the date as it means you actually went out of your way a little to think of them, but most people do have their birthday on there. They get tons of birthday wishes and are very unlikely to remember exactly who did or did not wish them a happy birthday.