Do men and women have the same number of ribs?
Yes. Men and women both have twelve pairs of ribs, for a total of twenty-four.
This question is usually raised in connection with Genesis 2:21, in which God takes one of Adam's ribs and uses it to create Eve. The assumption is that this verse implies that men have one rib less than women.
The verse actually implies nothing of the sort. Supposing for the sake of the argument that Eve really was created from one of Adam's ribs, there are at least two plausible scenarios. The first is that Adam started out with an extra rib, which was removed to make Eve; Eve, in turn, was created without that extra rib. The second is that Adam did, in fact, have one rib less than Eve, but this was not passed along to his male descendants. After all, somebody who loses an arm nowadays isn't doomed to have armless children.
(As an aside, there is some question as to whether the Hebrew term means "ribs" or "sides" in this context. But that's another matter entirely.)