I think about this a lot. No one can predict what will happen, but I don't see how it could possibly replace fiat currency. Governments are financed by debt, which they want to issue in a currency they control. The US gov does not want to issue bonds in a currency that they can't debase. That would be risky.
So, since they must issue bonds in dollars, they must also pay interest in dollars. They get this money from tax revenue. But that means they can never allow people to pay their taxes in anything but dollars, because they would risk losing money to volatility.
That in turn means that Americans will always need dollars no matter what, which means that they in turn have to careful about accepting something that's volatile with respect to the dollar.
So maybe it'll be a secondary currency that people use for certain discretionary things, where transaction costs are otherwise high, or when bitcoin is high against the dollar. But people will always have to think about what bitcoin is worth in terms of their countries fiat currency, and someone must take the volatility hit.
That doesn't mean it couldn't be useful as a store like gold. But there bitcoin faces strong competition because I don't think it will get much of a network effect if that's it's main purpose.