At some point in the not-so-distant future, a nation will issue its own crypto-currency that is exchangeable one-to-one with its ordinary currency. If Bitcoin really does have transaction advantages beyond ordinary banking and credit cards, this more stable currency will share those advantages but also have a MUCH simpler exchange process into a real-world currency.
Why would a national crypto-currency be more stable? In the old days, gold was considered most stable in value and its exchangeability with fiat currency made the fiat currency more stable. Fiat money is considered more stable in value than crypto-currencies and can stabilize their values.
Once some smaller nation has established the first national crypto-currency, it will be obvious to the nations with dominant currencies (and the banks and the credit card companies and the rest of the financial industry) that they need to do the same thing to protect the demand for their currencies.
As national crypto-currencies develop, the value of Bitcoin will plummet. Even the rumor of these currencies will make Bitcoin plummet. National crypto-currencies will keep transactions traceable to prevent money laundering and other evasion of laws, leaving Bitcoin with primarily black market transactions. At that point, Bitcoin will be regulated out of existence if not simply made illegal.
How could Bitcoin be eradicated by governments? Very simple: use market mechanisms! Set up a privateering system whereby Bitcoin usage that is caught results in confiscation, with the booty split between the government and the privateers. Libertarians often like to talk about pirates as anarchist entrepreneurs that created complicated organizations without government, but they conveniently forget that government licensed pirates (privateers) were also very common.
[Update 2/4/2014] The Paperless Economy: How governments can and should beat Bitcoin at its own game. Miles Kimball at Slate presents another good reason why governments such as the US might want to switch from paper to digital: to allow better control of interest rates and thus better control of the economy.