The Department of Planetary Science pays for your student health insurance, provided that you are a research or teaching assistant/associate employed in the department and in good standing. The coverage that is provided is the Student Health Insurance plan through the University's Campus Health Center. For more details on what is covered and not covered on the plan, please visit the Campus Health Fees & Insurance page.
Although the department pays for your coverage, you are responsible for enrolling yourself in the insurance coverage. This is done through UAccess -- be sure to do this before each semester starts! If you were enrolled for the previous semester, the program will auto-enroll you in the current semester and send you a helpful email to let you know that it has done so.
The current health insurance plan does not cover vision and dental. You can visit the GPSC's Health and Wellness Resources page for suggestions on alternate providers. Note that you can pay $25 to enroll in a "Dental Discount" program, and they'll send you a membership card soon after. You can show the card to participating dentists and receive significant discounts, though you still pay out-of-pocket. If you do this (it is absolutely worthwhile, usually even for a routine dental cleaning appointment!), confirm that your dentist participates in this program.
If you are on the NSF GRFP fellowship, your insurance costs will also now be covered (as of 2013, but check to make sure...).