My prediction is that Bitcoin (or some other alt-coin/cryptocurrency) will eventually become a single worldwide currency. It's reached a point where if a government tries to regulate it too tightly, they will effectively be shooting themselves in the foot and cutting their country off from outside trade.

The result is that the cryptocurrency will continue to gain momentum until it is used everywhere worldwide. This will eventually lead to a single worldwide government or an agreement between all countries across the world to act uniformly in regards to the currency. This will become a necessity to properly administer taxes and/or settle cross-border contract disputes.

Once you have a single government, worldwide government ids will be initiated (or all local ids, like driver's licenses will require integration with a wordwide database). At this point, the single government will then co-opt the cryptocurrency or initiate a new cryptocurrency and require everybody to tie their id to their cryptocurrency usage. The reasoning will be to crack down on crime, tax evaders, etc. Because it's a one world government or all governments are working together in lock-step, they would then have the capability of controlling/banning the cryptocurrency. Anyone not properly linking their identity to the currency will be breaking the law, and it will be very difficult to participate in commerce because there will be no more physical cash or coins.

Either way, the only way I see this playing out is a currency that most people assume was initially intended to break from government control will eventually lead to ultimate government control.

As a side note, I realize the concept of a one world government is controversial, but my personal opinion is that it is an eventuality.