Are there any laws or regulations that forbid pregnant women from participating on a cruise? Or does this vary from organization to organization. If so, are there any common rules?
As with airlines, cruise lines each have their own regulations. It appears to be fairly common that pregnancies later than 24 weeks (=6 months, i.e. 3rd trimester) are disallowed, or at least discouraged. This is earlier than for travelling by plane.
allthingscruise.com has an extensive list of regulations, though it may be advisable to contact the cruise line directly.