I think it's important when it's a child, but after a certain age, celebrating on a weekend is fine, too.
While I try my best to do so, it doesn't always work out that way.
Well of course their birthday should be celebrated...celebrated as in people giving them recognition. But as far as an organized party goes? I think that kind of thing happens when those being invited could at least stand a chance of being able to attend.
We always celebrate the birthdays whenever everyone can get together. It's hard when a BD falls in the middle of the week so it's usually celebrated on the weekend. No one has ever felt bad about it.
Kids don't care as long as they get attention, presents and cake on any day near their birthday. The weekend is fine for birthdays, it makes for a better celebration than on a school night. We celebrate different days, Christmas, Easter, etc on different days all the time. It makes it a lot easier of families who have to share the holidays with the in-laws.