The dentist that I was taking the kids to had individual rooms and also a big group room. My youngest kids (3 and younger) at the time would be seen in the private room with me. I sometimes had to hold them, and the littlest ones would be held down across my lap, with their head on the dentist's lap, to be checked. Older kids would be seen in the big group room, so they were independent of their parents but also weren't in a private room with a dentist and no witnesses. It worked fairly well, and my oldest loved being independent. I'm assuming that if the kid needed more than a cleaning and tooth check, they'd have it done in a private room though (for filling cavities, root canals, etc.).
My daughters take gymnastics, and the lessons are in rooms that only the child can enter (unless it's a Mommy and me class for the littles). The rooms have big windows to the main hall where everybody waits. The only problem is that the kids can see their parents through the windows. Sometimes this isn't an issue, especially with older kids, but younger kids are apt to show off when they see their parents watching, or just be distracted. My husband thinks, for the insane price we're paying for gymnastics instruction, that it would be nice if they'd put one of those one-sided films on the window so that the parents can see in but the kids can't see out.