While this may depend on the university/college type, health insurance is usually required for full-time students unless you can prove that you have other coverage.
For instance, see this page from the Ohio State University.
I would suspect that student health insurance will not be as good as many company-provided plans but may be cheaper since the overall health of the student population should be relatively good. Then again, maybe not. OSU's family coverage for student, spouse and 1 dependent is $9756 for two semesters. Summer adds another $2439. If you have department support as a graduate student, they may cover 85% of your health insurance fees.
A big university may have options for inexpensive care even if it's not covered by the insurance like if there's a dental or optometry program. There may be low-cost clinics.
Right now, your answer is probably too broad as the details will vary depending on the university.