I'm not a libertarian, but I think there is a lot to be said for libertarianism, mainly from the standpoint that there are lots of activities that the government just shouldn't be involved in. (Also, as political ideologies go, it's one of the more straightforward and consistent ones.) For any kind of market-based activity, I think that it is reasonable to view non-intervention as the default, and only to intervene if there is a compelling reason to do so. I find that some libertarians are dogmatic (although I couldn't claim there is a greater propensity to dogmatism than that of conservatives or liberals), with a stubborn adherence to the idea of personal liberty and insufficient regard for the practical consequences. Robert Frank describes a "rational libertarian" as someone who places a very high priority on personal liberty, and wants to be as well off as possible given that preference. I.e. for these folks it is more a practical than a philosophical issue. There was a long exchange on the Cato Institute's blog about libertarianism, and I didn't find the focus on fine philosophical distinctions very useful or interesting.
One area where I would part ways with hardcore libertarians is mitigation of externalities. This calls to mind Milton Friedman. He called externalities "neighborhood effects," and claimed (rather blithely, I think) that the costs were generally small enough that there would be no benefit to government intervention. This was predicated on his strong belief that governments do not generally function well, and that anything they do is done inefficiently. There is no arguing with that general point, but I think Friedman took an extreme view. I often wonder if a government worker was mean to him when he was a child. The presence of an externality doesn't automatically justify government intervention, given that such intervention will always be costly. However, it is unrealistic to think that private actions like collective lawsuits can always accomplish as much as government mediation.
Another issue is monetary policy. I'm skeptical of the workability of a market-based money supply, and I side with the economic mainstream in believing that a central monetary authority can foster growth and stability. I don't take Ron Paul's claim that "inflation is theft" very seriously, since there are such obvious criticisms to which I haven't heard any response: that inflation only affects cash, not wealth in general; that it is easy to hedge against; and that the problems of deflation are much worse. One thing libertarian politicians have going for them is that it is easy to whip voters into a frenzy by talking about the evils of big government, even if those same voters do not recognize or support all of the consequences of proposed changes.
Libertarians support a drastic reduction in the size and intrusiveness of government, with state activity consisting of little more than protection of narrowly construed property rights. As I said in a previous post, I think that the libertarian vision of government (or any consistent vision) would be much better than what we have currently. Libertarians often point to the gross dysfunction of US government as a justification for limiting its size and scope: since the government does everything badly, let's have it do less. There are perhaps many different facets of how and why government does not function as we would like it to. For example, Ilya Somin argues in his forthcoming book that limiting government is the best response to voter ignorance.
What I don't see so much is discussion of how to shrink the government--how to get from our current state to a libertarian one (or maybe Somin talks about this; his book isn't out yet). It would be a major transformation, and if we are somehow able to accomplish such a transformation, then there are all kinds of candidates for where we might like to end up. Public support for libertarianism is based largely on the practical problems with big government, but the path to the libertarian state is theoretical. We can talk about what the best form of government is in theory, or what we can accomplish in practice, but it doesn't work so well to mix and match.
Related to the question of how to minimize government is how to ensure that it would stay that way. It's easy to see how government grows: power is amassed and entrenched, programs are more easily expanded than cut back, etc. Democracy is self-sustaining to some degree; democratic states tend to stay more or less democratic over time. But there is no automatic restraint on small government that ensures that it stays small. When we consider what we would like our government to be, I think that it is at least as important to think about how we're going to get to this superior state and what we can do to sustain it. There isn't much point in transforming the government if it will eventually revert to what we have now, or something else just as bad.