My "extremist" views, in no particular order:
* Third parties are a bad thing. The person who is elected to an office should get more than half of the votes. As a corollary, primaries should be looked at as a bigger deal, should be easier to get into, and should all occur on the same day for national elections. A series of run-off primaries should be held to determine the national candidate for that party. This would allow for the "vetting" of the candidate that takes place during our current goofy primary season, but people in Iowa and New Hampshire would have as much effect on the election as people in later-primary states.
* Everyone should be required to pass a citizenship course in order to become a citizen of the US, whether they're born here or not. Immigrants who become citizens are required to know something about America. Why aren't those who were born here through no fault of their own?
* There is no reason that I am aware of for anyone to believe in any deities or other supernatural things. I know that's not extremist here, but it's extremist compared to the rest of society. Children should be taught skepticism in school, without shying away from skepticism about religion. However, I wouldn't ever advocate it in that way outside a skeptic-heavy forum, because I realize most Americans would be against it.
* The only time it is acceptable to kill a self-aware human being is when they must be killed to protect another self-aware human being. If it is possible to protect the individual without killing the aggressor, killing is wrong. No matter what they've done (short of heavy self-mutilation resulting in them becoming no longer self aware, of course), criminals are still self-aware human beings. I'm fuzzier on when someone becomes a self-aware human being, but it's definitely after the second trimester, so I have no problem with abortion. Where I get extremist: I can imagine myself being convinced that it's ok for parents to kill infants up to a certain point, provided those infants are not self aware. I don't think I could be convinced that it's ok for others to do so, but it's more because of the effect on the parents than the effect on the infant.
* If my brain still works but I'm in constant, excrutiating pain, I want to live. If my brain doesn't work but my body is perfectly healthy, I am no longer alive, and my organs should be harvested. Once my brain dies, as far as I know I no longer exist. I want to continue to exist as long as possible, because pain is more enjoyable than non-existance.
* Funerals and burial rights are for the peace of mind of the living, not the dead, and there's no reason for the "wishes of the deceased" to be taken into account at all. That said, when I die, I'd like for any parts of my body that can't be used directly in helping people (organ transplants, etc) to be fed to something, used as fuel, or otherwise used in some useful manner. Spending money/energy to burn my carcass or wasting land to burry my carcass is an enormous waste. That hunk of meat is no longer me. If I could convince my living family members that it was the right thing to do, I'd like to treat the corpses of my family members the same way when they die.
* All human beings are entitled to a certain standard of food, shelter, and clean water, if it is possible to provide that to all human beings (which I'm pretty sure it is). No human being should live above that standard until all human beings live at least at that standard. However, I'm not sure what I'd be willing to do to make that a reality. Note I'm not exactly advocating pure communism here; I think there should be a safety net to keep people at least at that level, but hard work should allow you to rise above it.