Advisor's wife is having a baby, should we be getting him something?
A personal gift from you, as an individual student, is not expected, at least by European or North-American etiquette. It may be nice to pool with other students and group members to offer a small gift (either something for the baby, or something for the father). It'd be more customary to offer it after the baby is born, rather than now.

On the other hand, there is no strong expectation that you offer a gift. I.e., if you decide not to for any reason, he won't think it weird.