Some hospitals also have a policy that you can have a different number of people in the room during labor versus when the baby is actually being born. This makes sense on one hand since during the birth some of the available space will be taken up with hospital personnel. You may also have your guests asked to leave during certain procedures like vaginal exams or the placement of an epidural. This is definitely a question to ask when you are taking a hospital tour. You will also want to ask if this number is different if you have a c-section.
The vast majority of hospitals only allow one person in with mom during a c-section. Though some hospitals are a bit more lenient with a second person if that second person is a doula or another medical professional. Other people may not be allowed if you require general anesthesia.
If you are planning a birth at a birth center or a home birth, you will want to talk to your care provider. Some birth centers will have limits but others do not. At a home birth, the limits may be only on what your space will comfortably handle.
That said, just because you don't have limits, doesn't mean that you should fill the space to the gills. There are many things to think about before inviting people to the birth, including your children.