I already visited one campus (Johns Hopkins) and am planning to visit another next Monday and Tuesday (Brown). The Hopkins program only admitted a handful of students, so there was no formal visiting day. My potential adviser requested that I send her a list of professors I wanted to meet and things I wanted to see around campus. She set up my itinerary and it was great. Before arriving to campus I did a lot of research. I looked up all the professors research interests, read at least one article from every prof., and I developed a rough list of questions for the program as a whole and some prof.-specific questions too. I'm a bit of an overachiever, but I also do much better when I'm prepared. I found that many of the professors were impressed when I mentioned something about their articles and one even asked flat out if I had read anything he authored (then he suggested I buy his book too!).
I don't think it's required that you read every professor's work, but a basic familiarity with their research is helpful. Then you can incorporate your interests with theirs and cater your questions to their work. Also, remember that the visitation day is for your benefit. If you don't prepare beforehand then you may not know the best questions to ask to get the most information. You don't want to show up and essentially ask questions that you could have found the answers to online. Then you don't learn much more about the program than what they advertise.
Now, on the other hand, I mentioned something about reading articles prior to my visit to Brown to a professor from Brown and she kind of laughed at me and told me I was being very ambitious. I think it depends on the program and how much you need to personally prepare to feel confident. I found that over preparation made me feel more at ease because at least I could fall back on my question list if I couldn't think of anything to ask. At the end of the visit day you're so exhausted from meeting with professors and graduate students that it is nice to have some questions to fall back on.This visiting day is more structured since there are a lot of students attending at once. Usually there is at least one meeting with graduate students and this is usually pretty fun and you get to pose all the student-life questions.
That's a lot of information and I hope it's helpful.