I don't think it makes much sense to purposefully blow off someone birthday. Unless you know the person doesn't want it mentioned.
If you forget a birthday, it's a different story. To some people it's no big deal, others might be hurt by it.
When one of my closest friends forgot my birthday last year, I was a little hurt, but it's not like I was offended or made anything of it, except some "you're getting old and your memory is fading" jokes at her expense.