My experience is more like DanaJ's, though I would say I also see it happen now. It's not a strict separation--kids do come upstairs every once in a while, and occasionally adults go down to check on them--but to my knowledge the adults don't really get stuck in the basement playing with the kids. Maybe they spend a few minutes admiring something the child made, but then they come back upstairs. Or if the kids are outside an adult might take a few minutes and go pitch a few balls for them, but then the adult rotates out and comes back to the adults.
It does really depend on the ages of the kids, though--they have to be old enough to play independently, without worrying that they're going to do something unsafe or get into mischief. And certainly the hosts have to think of some parameters and make them easy for kids to understand--it helps if the host has kids who already know rules and can say, "Don't turn on the TV" or "Don't go over there."
Someone also mentioned that age is a factor as well. One couple at my party brought a 1-year old, who functioned at the party differently than the kids playing in the backyard. He didn't need any special activity or entertainment, and people took turns carrying him around while they ate and drank, which seemed like fun for both the adults and the baby. And, as Sammycat mentioned, babies may just sleep through an adult event. I went to a bachelorette party once where one of the ladies brought an infant in a shoulder-wrap carrier and the baby didn't really cause any sort of distraction. I wonder if there is a propriety about bringing a baby to a grown-up event, sort of as an extension of yourself rather than as a child that will require external food/entertainment/care?
I think this question can be a controversial one. On the one hand you have people who say, "Of course a mother shouldn't be separated from her child if they're only X age!" with X varying a great deal--that is, they wouldn't expect a woman to have to leave her X-age child at home to attend even a function billed as "adults only." The arguments are usually biological, IIRC--a breastfeeding woman can only go so long without feeding the baby, for example, plus at a certain age babies are easy to tote around unobtrusively and spend most of the time sleeping.
On the other hand, you have people who point out that every baby has the potential to start crying and ruin the adult mood of the event, plus the mom needs a place to change the baby, feed it, burp it, maybe change its clothes, she'll need to bring a diaper bag, maybe it would be impractical for her to be as dressy as the event calls for, etc.. So allowing mom to bring the baby, when even mom can't predict what all that will entail or how the baby will behave, could potentially change the tone of the adult party. And some people might not be comfortable with a baby being there at all, even if it was quiet.
I remember a thread here a long time ago about a cookie exchange party, which was deemed no kids allowed but the hostess decided to allow someone to bring their very young baby. One of the other guests found out and was like, "Um, don't babies, like, cry and stuff?" The hostess was kind of like
babies cry!" but someone pointed out that the guest was probably just expressing their discomfort with the idea of the baby being invited, when they'd been promised no children would be there.
Whichever way a host decides to go, I think a guest should never presume
their baby is invited, no matter how young. If they check with the host and the host is cool with it, in the sense of, "Oh, I just assumed of course you'd bring her!" then the guest is fine to do so. But the host
should consider how this might change the dynamic they're going for.