One of the most important ways of thinking about the way that technological and commercial forces create change is Clayton Christensen's notion of a Disruptive Technology. According to Christensen, new technologies generally start by serving a niche market that is currently under-served by the incumbent technology (and the companies that sell it). The new technology is ignored by the incumbent companies because they can't see how to make money from it; it doesn't fit their big profitable customers and the niche market is too small to be interesting. So the incumbents ignore it. Meanwhile the new technology matures and improves to the point where it can be used by the big customers, and then suddenly the incumbent technology (and the companies that sell it) are obsolete.
Like any model of a complex situation this doesn't cover every angle, but its interesting to look at Bitcoin from this perspective. Christensen's approach in his book is to look at the problem from the point of view of a manager in an incumbent company (who sees a disruptive technology as a threat) or a start-up company (who sees it as an opportunity). I'm simply going to look at the major market forces, and in particular the niche markets that Bitcoin might serve better than the incumbents, and the possible paths out from those markets.
An obvious group of people who are served poorly by the incumbent financial system are criminals. Unlike most markets this is a matter of deliberate design. Over the past century governments have systematically regulated all forms of financial transactions in ways that make it difficult to hide ill-gotten gains, or for that matter legitimately-gotten gains that might incur taxes. Banks are legally required to know who their customers are and report any transactions that seem suspicious, or merely large. For people who move millions of dollars around there are methods to avoid such scrutiny, but these are themselves expensive; the necessary accountants and lawyers don't come cheap. Hence there is a significant group of people who have a pressing need to avoid the scrutiny that comes when you move tens of thousands of dollars around the world, but who can't afford the infrastructure used by those who move millions.
Traditionally these people have used cash, but that is hard to do across national borders because you have to physically move the stuff, making it vulnerable to interception by the authorities or thieves. So Bitcoin, with its ability to slide across national borders without trace or cost, is very attractive.
The Grey Market
A related group are those who deal in stuff that is legal in some jurisdictions but not in others. Porn and gambling are two major businesses here. Certain drugs also fit into this category, but you can't move the product over wires, so it is vulnerable to conventional methods of interdiction (although that doesn't stop everyone).
Governments trying to control porn and gambling have generally followed the money. This tends not to work well with porn because there is too much available for free. But gambling needs to move money to work, and so authorities in several countries have attacked it at this point. Hence Bitcoin is very attractive in this market as well; punters can easily convert their local currency into Bitcoins, and if they manage to win something then they can convert their winnings back almost as easily.
This is a catch-all term for people who have no access to conventional bank accounts, and hence have to deal in cash or barter.
Financial solutions for these people have traditionally been expensive and piecemeal. Moving money long distance is done by wire transfer, with hefty charges and the need to physically pick it up. Cash is difficult to hide from brigands and corrupt officials. Credit can be available, but only at punitive interest.
Things have improved; across Africa variations on themes of microfinance and mobile phone banking are changing the lives of millions, but they are still vulnerable. Local laws can limit access, and accounts in local currency are vulnerable to inflation. A stable currency that can be easily hidden and transferred quickly over long distance could meet a real demand, although it still can't provide credit. Mobile phone credit is already serving this role in some places, so something that is designed for the job should be readily adopted.
Actually holding Bitcoins requires rather more computer power than the many third-world mobile phones can provide. But that is unlikely to be a problem for long. If MPESA can have an app, then so can Bitcoin.
Bitcoin looks like a classic disruptive technology: it has multiple niches in markets that are under-served by conventional money, and the grey market and the unbanked provide a ready path up to higher-value markets in places that are now reasonably well served by cash and credit cards. The black market will also provide market pull for Bitcoin uptake, but if that were the only early market niche then the mere use of Bitcoins would raise strong suspicion of illegal activity. The presence of legitimate, or at least lawful, uses of Bitcoin provides a rationale for those offering to extend conventional services to Bitcoin users and plausible deniability for those whose Bitcoins have in fact come from illegal operations.
Accordingly we should expect to see Bitcoin become a strong force in finance over the next decade.