It's a great question - Marc Andreessen has addressed this question a couple times, and one of his analysis (if I've read it correctly) is that the only "inherent" value in Bitcoin is the value that comes from it serving as a transactional currency. I've probably bought bitcoin about a 15-20 times, and every time for the sole purpose of purchasing something. I didn't care (and the recipient didn't care) whether bitcoin was $0.00001, $1, or $1,000,000 a bitcoin - it was irrelevant to both of us. All we really cared about was whether it was non-volatile.

If that's the long term future for Bitcoin (as many people believe it is, and ignoring the value of the blockchain as a contract / consensus based negotiation mechanism for a moment), then the Bitcoin's value will eventually settle on a level that reflects its long term transactional use and "time in flight" - there is a non-zero period of time between when I purchase the bitcoin, and the recipient translates it back into local currency, in which the bitcoin will need to be purchased. Take your total daily transaction volume, and that time in flight - and you start to get a good sense of what the inherent value of bitcoin is.

That's the simple story as to why people are comfortable purchasing and holding it - it's going to be the global digital currency of choice, and as transaction volume increases, the value of the bitcoin will increase.

They are a unit of exchange that freely floats based on the demand for that unit of exchange.

There is an eventual fixed supply of coins (21 million), with currently ~13 million in circulation (http://blockexplorer.com/q/totalbc). Given that the 13 million isn't increasing at any meaningful rate as it relates to the money supply, we can almost consider the supply fixed (at least on any short term perspective).

With this fixed supply, if more people become interested in using bitcoin as a unit of exchange and buy it in order to use it, then they will increase the demand and thus the price. If they used it to transfer money back home (i.e. remittances), and their family their exited the position back into cash, then the demand would be neutral. In reality, their is some cost of carry where by holding it for a period, you still increase the demand.

That would an explanation for the price were it governed by an actual underlying value.

In reality, the price is mainly governed by speculators hoping that it will be used by people as a unit of exchange eventually and thus the speculators are buying and holding coins.

Human nature. Hoarding, speculation, pain-avoidance ("could have/should have" 10yrs from now)... emotion. It's wonderful! The price is a reflection on our thought processes.

Where does the value of USD come from?

A couple hundred million people are required to pay taxes using it. That implies that there is some inelastic demand for dollars.

That factor alone obviously doesn't prevent every currency collapse, but it is a key difference between "government fiat" and "geek fiat" currencies.

The monetary supply is tailored to the needs of the economy to prevent volatility and create value. By being able to buy or sell anything and have the currency worth a predictable amount there are many transactions that can happen that would not be possible with a more volatile currency.

Ask the same question of a fiat currency, say, the USD.