Recent report have suggested that Bitcoin could go as high as $1 Million USD per Bitcoin.
An examination of traditional currencies, with particular focus on the US Dollar reveals massive quantitative easing over the last five years. This means that governments are flooding the markets with additional currencies, severely devaluing the money supply.
Governments have simultaneously adjusted their methods of calculating inflation by removing the food and energy components. This is insane, as food and energy are the two primary items that people need to live!
When the bottom falls out of these fiat currencies, people will be looking for alternatives. Gold is one such alternative, but governments have historically seized gold during times of currency collapse in order to force people to hold their worthless currency and to give the government hard assets to run their operations on.
This means that cryptocurrencies (like Bitcoin) will be the safest place for investors to put their money. And because of the relative anonymity involved and storing and using bitcoin, the ability of governments to seize it is limited.
And because the supply is limited, very small purchases of BTC on the open market can lead to massive price swings.
It's possible that due to this limited supply, a collapse in the economy could lead to such an overwhelming demand for bitcoin, that we could see prices as high as $1,000,000 USD per bitcoin. Of course, in the scenario I described, those dollars won't be worth as much as they are today, but a million bucks is a lot of money no matter how bad inflation may be.