Anarchist perspectives are going to range widely on this from that put forward by Iconoclast to people who reject the idea of universal health care as an outright expansion of state control and authority. I tend to fall towards the latter personally.
I want to be clear: I believe that all people should be able to access the things they need to survive, but I do not support creating more infrastructure and bureaucracy to do so. In particular the model that has been put forward by the Obama administration is really troubling to me in that it uses economic coercion to create the conditions necessary for it to work - you can't opt out. Anything the government (or the workers, or whatever) forces upon us is anathema to my conception of anarchism.
In addition, I am actually wary of any health care that looks like that we understand as western medicine - invasive medical procedures that rely on experts, the spread of super viruses and antibiotic resistant diseases, the increased reliance on technology to prolong life, and so forth make me extremely uncomfortable. To my mind, much of what passes for health care in our society is really trying to fix the problems of industrial civilization through more industrial civilization, as well as being founded on an overwhelming desire and drive to avoid death. At. Any. Cost. Essentially this point boils down to: jettison industrial civilization, and we likely jettison many of the current health problems people face. Sure, some things that are now easily treatable will be more deadly, but, to my somewhat dependent on the medical-industrial complex self, that trade off seems worth potentially exploring.