Like so many things in Costa Rica, the answer is "It depends".
Costa Rica has socialized health care. It's very cheap ($45 a month or so IIRC) and the care is pretty good, however the waits in the doctors offices can be an all day affair in many cases.
There is private health insurance as well. Your US health insurance won't cover you down here in most cases, though they may have an option to airlift you out for treatment back home. It will probably be expensive.
There are a number of international health insurance providers, such as BUPA international. You can get a quote online pretty easily, just go to their web site
http://www.bupa-intl.com/. This is not an endorsement, i've never used them, so I don't know how well their service is, and there are others as well.. a google search will find plenty.
Healther care insurance (even international) is cheaper in costa rica because health care costs are so low here. VERY low. even at private hospitals like CIMA (which is affiliate with Baylor University Hospitals). The biggest reason is no medical malpractice lawsuits.
I basically keep catastrophic insurance, and just pay out of pocket when I need to go for minor stuff. It costs a lot less that way for me. A typical doctors visit is $50-$75 here.