How much do Interviews and getting interviews matter?

It really depends on the school how much weight they have. Using myself as an example I applied to private liberal arts colleges and they all recommended interviews but they weren't required. I felt I had a few gaps in my application so I feel the interviews definitely helped clear up some things and gave them extra information they wouldn't of had otherwise which is always good.

Unless it is required interviews don't usually have enough weight to break your application unless you do or say something really untasteful like bashing others, making excuses for things in a way that doesn't show you grew/learned from it, etc.

Usually the interview doesn't matter too much. Since some applicants are doing it and some aren't, the interview is inherently not as important as the transcript, activities list, essays, and recommendations. However, DOING an interview can matter. This shows schools that you are interested in them enough to spend 30 minutes talking to an alumni and learning about the school. Furthermore, the school can see that you are a real person who has feelings, not an academic robot. So I would say request an interview whenever you can, and if they offer it to you, definitely take it.