The possibility of a currency collapse has plenty of historical precedent. And it might lead to a number or outcomes. Currencies collapse all the time, but it has been quite a while since the United States experienced a currency collapse. There is a difference though from previous experiences with currency collapse today though, since the American Dollar is the reserve currency for the rest of the world. I have seen this referred to as "Dollar Hegemony," and it gives the U.S. dollar a very special status when compared to other countries. When you hear about talks regarding a creation of another system for a global reserve currency (usually a "basket" of national currencies), what they are talking about is creating a currency to buy goods with globally. Essentially a reserve currency is the currency that all exporting nations accept for their goods. So, consider a small country, say Thailand. Now Thailand has its own currency for in country transactions (the Thai Baht), but if Thailand wants to buy Oil from, say, Nigeria. Nigeria has its own currency as well, the Naira. Well, turns out that Nigerians aren't too keen on holding Baht, because, well, if they want to buy things that Nigeria doesn't have, they have to convert the currency to the currency of the nation that does have the stuff they want. Given the number of countries out there, and the large differences in economic scales, global governments decided to settle on U.S. dollars as the universally accepted money.
This has clearly served the U.S. well since implementation, and I'd say it has served the American people well. Looking at it from a global perspective is a little trickier though. Not the point of this ramble though, so let's stick to the American perspective.
Right now the U.S. is going through some tough economic times, and there are issues underlying that which Americans simply don't want to face up to. Now much of the issue has been about globalization and a phenomenon called "Wage Arbitrage." With improved communications technology allowing knowledge workers to corroborate with lower wage (but similarly educated) counterparts overseas, competition is fiercer, and wage arbitrage can hit virtually every level of education. And our educational system is not designed to create entrepreneurs from an early age, but rather it seems to be designed to create middle management. Now management is certainly important, but it is also becoming more and more fungible.
Worse though is the fact that the U.S. government has become addicted to easy credit, and made financial promises that are going to have to be rescinded, or at least substantially restructured. Whether it is possible to elect a leader that truly makes those reforms a priority remains to be seen. But whether they campaign on a promise to do so or not, the other problem is that there is a limit to how much lending the rest of the world is willing to do, and there is a limit to how much the structural deficit can be monetized.
What I do expect is an extended period of inflation along with wage readjustment, followed by a requirement to further borrow from the global markets, and such borrowing will be met with specific austerity provisions, forcing whatever government is in place at the time that happens to face the prospect of default, or implementation of austerity measures, which will give them some level of political cover to implement the austerity measures that will satisfy global creditors.
There are other possible scenarios, but I see this as the most likely. Of course, if this scenario does play out, savings is not a good place to have your assets parked in. The trick will be to identify producing assets that have long term production value that are not already overvalued. International real estate, manufacturing, and of course precious metals and energy remain viable options. Land with some productive value is likely always going to retain some level of value. Precious metals can crash unless they have industrial usage as well (and for this, I see silver and Platinum as the real hedges, but Gold has the rep). Energy has some exposure to technological innovation pressure, but the infrastructure for an oil dependent world is expanding, and unless you feel you can credibly identify a next generation energy play, I think that Oil will remain profitable, with usurpers taking long enough from an infrastructure point of view to be able to unwind should the markets move away from oil due to some sort of technological innovation.
But expecting a U.S. dollar currency collapse in the next few years I see as highly unlikely. Envisioning a credible scenario for that is difficult, and I expect it requires a severe global crisis that likely looks like a serious hot war that draws in the U.S. and either China, or potentially the EU.