As a complexity theorist, I recognised the significance of bitcoin almost immediately. Bitcoin is a superior medium of exchange to what we have been using.

1: Enforcement of anti-counterfeit rules is built in.
2: No central control means that the intelligence of the market rules, and it is a difficult medium to be abused by elites.
3: Freedom and inexpensive exchange
4: Math says that currency monopoly is unhealthy, so there needs to be competition in currency.
5: Designed to reward the early adopter.
6: Bitcoin mining with opencl is cool.
7: Bitcoin mathematics is at its foundation beautifully conceived. Rather than using policemens guns to enforce the nature of the currency, mathematical and computational law do that naturally.
8: There are complaints that bitcoin has no inherent value... Believe it or not, this actually is an advantage because it bypasses one of the money-mongers primary strategies... They find ways to take the currency in use out of circulation (such as government decrees that no one is allowed to have gold) so that they can force people to use their junk shit vomit currencies.  For currencies with inherent value, it is difficult to impossible to replace them, so the public  winds up falling into their trap. Bitcoin is not that way.  It can not reasonably be stolen out of existence. In the worst case, they can just start a new bitcoin. 
9: The current system is shit, designed to make slaves of people, and its the responsibility of smart people everywhere to assert an evolution.

Ofcourse, BC has weaknesses as well. Everything does,  but that was not the question.