As a libertarian, sometimes I like democracy and sometimes I really deplore it. While it is a widely misunderstood subject, most libertarians understand the negatives of democracy. It is majority rule, which violates the rights of the minority.
The United States was (or should I say "United States were") formed as a constitutional republic. While there were certain democratic elements (in the form of voting) instituted as part of the republic, there were also a lot of anti-democratic pieces put in place. The 1st Amendment itself is anti-democratic. Congress shall make no law regarding speech, religion, etc. It is only because there are people in the minority who speak and practice religion that aren't popular that this is written. The majority usually doesn't need protection (although that is not always the case).
Even many of the elections put in place were not completely democratic. Prior to the 17th Amendment, U.S. senators were selected by the state legislatures. They were not directly elected. And, of course, the president is still selected by the Electoral College and not a direct popular vote.
So philosophically speaking, it is natural for libertarians to be against the idea of democracy, particularly when it is defined as majority rule.
Ironically, Americans would be much better off in some respects if the idea of democracy were actually followed. A majority of Americans are against the wars overseas, yet they mostly continue (even in Iraq).
I would use the idea of a balanced budget as another example, but in this case, Americans are also against spending cuts to their favorite programs. So that tends to be more of a contradiction. It probably isn't possible to have a balanced budget without drastic spending cuts. So with this, it is obvious that politicians will choose bigger government and no spending cuts, given a choice of the contradiction.
While this may sound a little cliche, it is true that democracy does somewhat keep the peace, at least within a country. We have the peaceful transition of power. Since most people accept the premise, there is little or no violence that comes with each election.
Aside from the idea that minority rights are at risk under democracy, I think the biggest negative to democracy is that it enslaves people who think they are free. Most Americans think they are free because they can vote. But when you have the choice of Statist A vs. Statist B, what good does it do? And if some kind of a fluke happens where someone powerful takes on the establishment, then the result is something like the JFK presidency.
As a side note, I don't fear any one person becoming dictator in the U.S. Why would the establishment allow this to happen when it would give up their cover of democracy?
In the long run, I'm not sure how much the idea of democracy matters. I don't think voting will change anything until there is a major shift in the American mind. While this shift has already begun, we are still a long way from having tens of millions of libertarians.
It all comes back to education. The more people that are well-versed in liberty, the more liberty that will ultimately prevail. The politics will eventually follow the American mind, regardless of who wins the elections.