Disclaimer right up front: I personally doubt that Bitcoin will be a long-term success. I fall into the camp of people who believe it is not a mature enough technology, unproven despite the hype. It is much too volatile to be any good other than as a risky investment, though if you time it right, you could stand to make a fair profit at the moment.
What I do think is very interesting about Bitcoin is that it is a harbinger of things to come. It won't replace greenbacks anytime soon, but I think it's an indicator of where the world is heading.
I believe the global and historical trends we are seeing right now is away from traditional authorities acting as monoliths, in favor of empowered individuals. We are most likely at the very beginning of the trend - I doubt anyone reading this board in 2013 will be alive to see the transformation completed. But we will be alive to see some very interesting changes. Generally speaking, all centralized authorities, be they monetary, political, technological, etc. are fracturing in favor of empowered individual actors. That poses challenges as well as opportunities.
For example: consider a technology like Square coupled with a store of value such as Bitcoin. (In this example, the terms "Square" and "Bitcoin" are just placeholder values for mechanisms and tools). Oversimplifying greatly, if we take these technologies to their logical extreme, we have the tools for an individual to completely bypass banks and traditional governments. You have some goods that I want, I have some Bitcoins, we do a point-to-point transfer; you get the money, I get the donut, end of transaction. Truly savvy users in this system will have their own way of transmitting the money from themselves to the merchant. I'll choose to trust someone like Square to do it safely and securely for a nominal fee.
Whether or not you agree with the mechanics of how this happens isn't really the point. The point is to show that we are heading towards a future where two individuals can transact freely without a middleman "getting in the way." For the purposes of this discussion, "getting in the way" means limiting the freedoms of those individuals to transact as they please.
Of course, there are problems with this. If there are no rules, inevitably someone will game the system or take advantage of someone else. That'll be unpopular, and so people will seek to band together to transact in a network of trust. The idea of a network of trust is important today, it's value will only increase over time. I can't remember the exact term, but I read a wonderful book some years ago called "Anarchy, State and Utopia" which dealt with the philosophy around these types of issues (it's a pretty academic book, but here's a link in you'd like to see - http://amzn.to/18883MU - and yes, that's a kickback link).
Boiling it down, the main argument I took away from that book was that, even in a world where there are no "governments" as we're used to thinking about them, we'll never achieve true 100% freedom because there'll always be those who are stronger who take advantage of those weaker than themselves. For this reason, people join together and form mini-states. Within those mini-states and associations, rules will exist that people choose to live by, limiting individual freedom to provide security.
I think people are right to be excited about Bitcoin, but I'd be cautious about heralding any brave new world within the next 25 to 50 years.