I think it depends on the school. If you go to a big state school with a huge facility, you will likely have access to that for x amount per semester. My undergrad was a large state school, and you went there for everything. It was the same deal for undergrads and grads. They had all sorts of specialists, and only send you off site if there was a unique problem.
My current school has about 10,000 students (undergrad+grad) and they have a clinic for the routine stuff ($150 per year), and offer health insurance for the bigger stuff ($1,000) per year. Anytime you need to see a specialist you go to a private doctor.
So - I think it depends on the size of the school, as well as whether they are connected with a medical school.
You can usually find private plans for $100 a month or so, but the price goes up tremendously with pre-existing conditions. I have a pre-existing condition and it was WAY better for me to take advantage of the school insurance.
I do remember a few posters on here last year complaining that their school didnt offer anything - so I would definitely check with your school for details.