Yes, this is common. This is called "post-pill amenorrhea," meaning there is no period for a while after stopping the birth control pill.
The Pill works by suppressing the pituitary gland's cyclic stimulations of the ovaries. In essense, the Pill makes the pituitary gland think you're pregnant, so the ovary is not stimulated to ovulate every month. When you get off of the Pill, the pituitary takes some time to snap back into its cyclic relationship with the ovaries. Also, the return to normal may be piecemeal in that you might be stuck in the first half of the cycle, the more "estrogenic" half, giving you tender breasts, slight nausea, and all of the symptoms (along with the late period) that may make you think you're pregnant.
It's a mess, but it is a self-resolving mess. Most women are back on track with normal cycles within three months, but some rare individuals may take as long as two years to return to normal (though this is very rare and not a reason to avoid the Pill if you need contraception).
Now for the tricky part. If you have post-pill amenorrhea, it cannot be predicted whether you'll have a period first or ovulate first. So if you're comforted by the fact that you're probably not pregnant because you know you're experiencing post-pill amenorrhea, keep in mind that you might just ovulate first, conceive, and go on your pregnant way still thinking you're in amenorrhea.
So it's a good idea to periodically (no pun intended) do a pregnancy test with your healthcare provider.