I do not claim any special expertise on Bitcoin, but because it is in the news, I will weigh in. As I understand it, Bitcoin is a digital currency that exists only as electronic ledger entries. It is "mined" by doing complex mathematical equations to qualify for a bitcoin. The makers of Bitcoin have put a ceiling on the number of bitcoins that will be released. It is beginning to spawn on-line imitators. Oh, yes, and its biggest fans tend to be libertarians who hate central banks.
In some ways, this is downright amusing. After all, one of the big complaints Austrian-style libertarians have about central banks is that they reject the intrinsic value of gold and instead issue fiat money that is just so much designer toilet paper. But really gold is fiat money too. You can't eat it, burn it, wear it or build with it, and it is too heavy and too soft to make good tools. It is useful to plate against corrosion, conduct electricity, and various purposes that call for a highly malleable and ductile metal. And bitcoins are the ultimate fiat money, not even useful as designer toilet paper. Granted, bitcoins have two other properties Austrian (or Austrian-esque) libertarians value. They will be released in a limited supply, which will protect them against inflation. And they are not controlled by any government. I suspect that libertarians may be in for a lesson in why these can be problems.
Certainly, Austrian-esque libertarians have an extreme aversion to inflation, which they see as an immoral confiscation of people's savings. They see opposition to inflation in absolutist terms, not as part of a complex framework of tradeoffs. (See here for a most amusing discussion of why prioritizing zero inflation above all else makes no sense at all). And they are not sensitive to the hazards of deflation. If bitcoin works as it is supposed to, it will constantly increase in value, which sounds like a good thing until one realizes that this means it will experience constant deflation. And libertarians may learn the nature of a deflationary spiral -- as a currency's value rises, people will be reluctant to spend it and its circulation will decline, causing its value to rise more until it becomes hoarded and ceases to circulate altogether. Fortunately, there will still be old-fashioned national currencies around, so the deflation of Bitcoin won't actually harm anything.
As for keeping the government out, Bitcoin appears to be going to the opposite end of anti-central bank libertarianism from the one that wants to rely on gold -- the one that wants to return to the free banking era. In the free banking era, there were government issued gold and silver coins, and sometimes even government bank notes. But these were not the only currencies. Each bank issued its own. If your primary goal is keeping government from having a monopoly on money because you think this gives government too much power, then I suppose free banking is an excellent system. If your goal is much of anything else, then the advantages of free banking are less clear. It turns out that private banks, if allowed to issue their own currency, are prey to the same temptation as central banks -- to issue too much. And private banks did, quite regularly, issue too much currency with all the evils that Austrian types warn about -- inflation, speculative bubbles, and a boom-and-bust cycle. In addition, bank failures were common, so that people who put their money in the wrong bank could lose their entire savings. People who accepted notes from the wrong bank might see them turn into designer toilet paper if it failed. Also, exchange rates between the currencies of different banks fluctuated wildly, so people never knew how much the money in their pockets would buy at any given time. (Financial newspapers posted exchange rates daily). Oh yes, and the system was rife with fraud. Otherwise, it worked very well.
My guess is that if Bitcoin succeeds and inspires imitators, we will see something similar happen with digital currencies. Many will succumb to the temptation to issue too much and see their digital currency endlessly depreciate. Others will resist the temptation and fall victim to Gresham's law; their currencies will be hoarded instead of circulating. Weaker currencies will fail and cost people their savings and not even leave them designer toilet paper. Exchange rates will fluctuate wildly. (They already do). And the system will be rife with fraud. A lot of people will learn the hard way why the free banking era wasn't so great.