Quite a few people have noted that the baby shower started out as an adults baby shower only. This was the time when mothers could get together without kids and spend a little time on adult conversation and entertainment. Since these people are mothers, they obviously like kids, but need a break from them once in a while!
So, how would that be put on the invitation? You can add a little note at the bottom that says, “Adults Only” or even give a short explanation that there is limited and assigned seating so children are not allowed.
Since this is only for a few hours, it seems reasonable that parents would crave a bit of kid-free time. As long as it is phrased clearly and properly, there should be no confusion and no hurt feelings either.
There is such a thing as a baby shower with kids. If it is difficult for some parents to leave their children home, maybe because the children are still very young or even breastfeeding, you could consider setting up a children's room with a sitter or two just to watch out for them. Outfit the room with a lot of child-safe toys, simple snacks, and even a sundae bar if you think it would be appropriate. That way, the adults can have fun along with the children and may even have a problem getting the children home!
The other side of the argument is that it is a BABY shower after all, so why shouldn't children be welcome? You could have what is called a family shower.
Young mothers would be the obvious guests at a baby shower and these mothers often have just had babies themselves. It would be rather difficult for them to leave the children especially if they are also breastfeeding.
It's considered polite for the guest to ask the hostess if they can bring their children, whether or not it is stated on the invitation. If the babies are small, it should be expected that they will invariably show up at a shower or a party. Since the baby shower is not as formal as let's say, a wedding, people tend to interpret the invitations very differently.
It also depends on how close you are to the guest of honor and the other people attending the shower. If you are all good friends, it's safe to assume that they will expect you to bring your baby and think it funny if you arrived alone. Babies are rather much easier to stash (that's what strollers and baby seats are for) and are a great way for the mommy-to-be to know what she's going to be up against!
So, babies or no babies? It would be safest to say that it depends
on the guest of honor and how she can handle kids when her hormones
are raging. If the guests are not comfortable with it, the politest
thing they can do is decline attending the party. It's just a baby
shower after all, there will always be another get-together and
celebration.