People looking at Bitcoin tend to fall into one of two camps:
1. Bitcoin is a bubble that will inevitably pop and become valueless.
2. Bitcoin is a disruptive technology following the S-curve most disruptive technologies do.
I fall into the second group (and hold a small quantity of Bitcoin). The current instance may be a bubble or may be an approach of its true valuation (that I believe is likely to increase due to Metcalfe's Law), but even if it pops, it has substantial long-term utility not met by existing technologies, so its ultimate value likely exceeds its current value.
First, I'd like to counter Gonzalo Lira's premise, that there is no market where you can exclusively use Bitcoin; I disagree, and in my disagreement, I will use this web site as an example, that contains a bot for tipping with Bitcoin. There does not exist another good way to see another Internet user, go "I want to give that guy some money," and give them money without one of you providing personally identifiable data. It could similarly be used for gaming tournaments or any other instance where all you have is an Internet pseudonym. Given that people experienced with the Internet are wisely reluctant to provide personally identifiable information to people they have only met on the Internet, Bitcoin addresses a real need: The ability to send money to people you cannot identify by their legal names. It has similar advantages for sending money "back home" for immigrants (and its rising price may increase its utility for this, particularly due to the arbitrage situation; Korea, for instance, hit $1500/XBT the other day).
Even if his premise were accurate, Lira would still be wrong. For instance, Bitcoin has additional advantages as a reserve currency not shared by contemporary currencies. While the dollar is the reserve currency of the world, the US government has an advantage: If they need to pay off debts, they can issue more dollars, devaluing it. You end up with the same problem if you transition to another nation's currency, and a comparable, but smaller, problem if you use a basket of currencies. Even gold has a similar problem: At some point it becomes economical to send mining space probes and extract gold from asteroids (see, for example, the Spanish conquest of Latin America). Bitcoin has an advantage here because of the known, fixed, limited supply (admittedly, it would have been better if it had been designed to scale with the size of the network for, say, 10 years, and then increase by 1%, giving you a stable exchange rate during its initial growth (now) and then a slightly inflationary currency afterwards; PeerCoin does something like this). This limited supply cannot be changed without agreement of the other members of the network. People have to have an actual economic exchange to acquire Bitcoin (which includes mining it, which is essentially an economic exchange in return for helping the network run smoothly), no one can just decide "Oh, yes, I have enough money to pay you now." That's far better as a reserve currency than any of the existing ones, because it does not require trusting a third party (an extreme weakness of most current currencies). This is likely to be attractive to world governments other than the US since it reduces the US's influence over them.
Bitcoin also has the advantage of storage; it costs no more to secure 100,000 Bitcoins than it does to secure 0.001 Bitcoins. Contrast this with physical assets, such as gold or oil, which require significant infrastructure just to put them somewhere, to say nothing of securing them. To have access to a given Bitcoin address requires the storage of 32 bytes, costing approximately $0.00000000149011611938 to store (for comparison, the value of the smallest Bitcoin unit is orders of magnitude larger than this cost). To store the entire Blockchain costs about $0.60, comparable to the transaction fee on a single $20 credit card purchase. The security can be via password, with all the standard password disclaimers, or physical, by storing a record of the private key somewhere and securing it the same way any piece of paper might be secured (store it in a safe, hide it in a book, have a really good memory, etc.). This is a tremendous advantage; the disadvantage being that since it has no industrial utility, its value is strictly in what other people are willing to pay for it--it's solely a matter of perception. This is a disadvantage over physical goods, but it's a disadvantage shared by any currency in a country where that currency is not required for paying taxes (staying out of jail being generally advantageous), and the dollar's doing all right for this, so that's not necessarily a deal-breaker.
Bitcoin is affected by Metcalfe's Law: As the size of the network grows, its utility grows as a square of the number of users (this is also why non-Bitcoin cryptocurrencies should be looked at with skepticism: unless their technology is so much better than Bitcoin as to trump the network effects, they aren't actually providing any value). This means while users grow linearly, utility grows exponentially. Combine this with something that grows in a linear supply and you'd expect to see an exponential curve in its value. This feels intuitively wrong, because most assets do not grow exponentially; my claim is this is a black swan event that is an asset that follows the S-curve and right now we're still on the rising exponential portion of it. Eventually it will hit saturation: Everyone who wants to use Bitcoin will be using it, and its exchange rate will stabilize, but right now there are, at most 22 million users, assuming that each address ever used belongs to a unique user (this has approximately a 0% probability). More realistic is that there are at least 2,161,563 users, which is probably still extremely low. In either case, very little of the population has ever used Bitcoin, but you could have said the same of the Internet in 1993 or Facebook in 2004. A stable Bitcoin would make it more useful for its general application, but it's impossible to both grow rapidly and be stable, so these are necessary growing pains.
Since Bitcoin is able to solve real problems not addressed by preceding technologies, it has value. As long as the rate of people joining the network exceeds the rate of Bitcoins being added to the network, the value of a given Bitcoin will rise. How much that value is is hard to say, but approximating its endgame market cap as comparable to gold (a reasonable guess, and I emphasize guess, based on its ease of storage) gives it an ultimate value of $185 billion, or another 15x increase. We are currently in the phase of nascent adoption, where people know what it is but haven't used it. Over the next few years, adoption's likely to rise just because it's cheaper to accept than the existing technologies. Its irreversibility is also likely to be attractive to merchants, particularly digital merchants.