Libertarians are just right wing anarchists. As simple as that.
I totally disagree - that might be many of whom have taken over the name, but it is clearly not the philosophy.
Libertarians take the personal liberty of the individual to the extreme. It sees government as a barrier to personal liberty, but also sees it as a necessary part of a federal and state functioning. So for the libertarian the challenge is where to 'draw the line' - they believe that there is a fundamental need or national defense, but definitely NOT 'nation building' like Bush did. They believe that protecting citizens from physical harm is necessary ... but it gets murky when it comes to non-physical harm.
Libertarians believe that the government has the duty to provide education, but mostly all they agree on is the '3 R's' stuff, and much of the 'extra' stuff (like art, music, etc) is considered personal enrichment outside of the scope of governmental duty.
They don't think that the government owes anyone a paycheck. Period. If you cannot pay for your housing, you live on the street. If you cannot afford food, you die. If you cannot afford medical help, bleed out. If you cannot afford to feed your children, THEY die and while you should probably learn a lesson, that isn't mandated.
For me, who holds with many of these views, the biggest problem is how the neo-cons and tea-baggers have co-opted much of this to use as a weapon against anyone who isn't white, male, Christian and heterosexual. But again, that has nothing to do with the basic tenets of the philosophy.
As a nation we decided a very long time ago that we were NOT a libertarian country, and this isn't a 'liberal' thing ... it is a 'pretty much the whole country' thing.