I'm not going to paste a ton of links for sources on this issue because Google exists, use it. There has been quite a lot of hoopla over the killing of Anwar Al-Aulaqi via predator drones. A member of Al Qaeda. So.. what's the issue? Well, he had American citizenship.
Skipping a lot of bullshit, the basic issue people are having is that he should have been arrested and given a trial due to his American citizenship. It's said, among other things, that his citizenship grants him Constitutional protections that should prevent him from simply being bombed in some random country. It sounds okay in theory but... I can't bring myself to give a shit.
I'm a pretty liberal guy, but as far as I'm concerned if you go sign up with a group like Al Qaeda and start plotting against the USA, you should probably expect a cruise missile to land on your head, regardless of your citizenship. Honestly, I don't care about the legal justification, I personally don't believe that you should be able to go to another country and join a terrorist organization and still expect your rights as an American citizen to remain intact.
If we refused to bomb a site because we knew one of the terrorists had American citizenship, what then? Do groups like Al Qaeda start recruiting people with American citizenship in large numbers so they can put one or two at every gathering and grouping to prevent them from being attacked? I don't buy it. Maybe I'm just crazy, but I really don't care about this issue in the slightest. If you want to complain about the government or people in power, there's plenty to complain about without bitching about terrorists being killed. Maybe I'm insane, but that's my opinion on this.
Update: Just wanted to clarify that if you're in your house in fucking Chicago with some unpaid parking tickets, I wouldn't consider it okay for the government to blow up your house. I think there's a difference between that and joining Al Qaeda and plotting terrorist shit against the country from some cave or bunker somewhere in Fartistan.