Different AmeriCorps programs have different insurance policies they provide- some are better than others. There are state programs that AmeriCorps members, and genearllly low income individuals qualify for.

Minnesota Family Planning Grant

You can apply for this at Family Tree Clinic in St. Paul.
http://www.familytreeclinic.org/clinic/mnfamilyplanning
(this site gives the qualifications, for example you need to make less than $1733 gross monthly income per single person)
Or at a Planned Parenthood location.
http://www.plannedparenthood.org/

The grant offers free access to birth control for a year. When your year is over, if you still qualify you can re-apply. You do need to be a MN resident. It also covers anything related to family planning.
Tip
I have been told by Family Tree, that if you need to make an appointment, ask how your health problem affects family planning, or just general questions about family planning. Then they count the visit as a family planning visit, and most likely you will not have to pay the sliding fee scale, and instead the grant will cover it.

Free Clinics
The Red Door Clinic in HCMC
Offers free STD testing. It is walk-in only.

General Tips
If your AmeriCorps insurance is too expensive and you need to see a doctor about a non-family planning related problem, try calling Family Tree anyway. They can tell you about sliding fee scale clinics in your area that may be cheaper than using your insuarnce. There are some that offer free services if you are below a certain age, for example below 23- so make sure to mention your age. A great one for example is the Indian Health Board Clinic in Minneapolis- which serves everyone.

If you need lab work done at a clinic that sends their lab work to HCMC (like Indian Health Board), when you get the bill from HCMC it will not be sliding fee scale. Call them and tell them you are poor and cannot pay, and they will cut your payment to a fraction of what it originally was.

When in doubt- tell people you are poor and cannot pay.