1. The US and UK should engage in a currency war with the EU.
The problem the eurozone has is that European Central Bank president Mario Draghi is fashioning himself as the man with a carrot and stick. He knows that monetary policy can't solve all of the area's problems, and that national governments need to step up and do something to help the situation. Sadly, the policy he wants is more fiscal integration, which most countries are terrified of.
If European governments fall in line, then Draghi would be likely to implement the monetary easing which could really help the continent. Unfortunately, given the integration he demands is not forthcoming (because Germany is terrified of taking on Spain's debt and Spain is terrified of being a vassal state to Germany), it doesn't seem like the ECB is going to make any positive moves in the short term, instead choosing to futilely dangle the carrot a bit longer.
So what is to be done? Well, a worldwide crisis needs a worldwide solution. The Federal Reserve or the Bank of England could unilaterally start buying up euros. Matt Yglesias writes :
If the ECB just sat back and relaxed, that would make Europe's problems even worse. But the most likely scenario would be massive retaliation by the ECB and much-needed transatlantic monetary stimulus.
Of course, it's true that this solution counts on the ECB reacting in a non-insane manner, which has only occasionally been a good betting strategy.
2. If you like stimulus so much, why don't you live there?
If the rest of the world wants a solution which removes agency from the hands of the ECB and Mario Draghi entirely, then ex-Federal reserve official Joseph Gagnon's suggestion, submitted to the Washington Post's WonkBlog , may work:
There are two other individuals who have the same power as Draghi to end the euro crisis: Ben Bernanke and Zhou Xiaochuan. The Fed could do the next QE3 entirely in Spanish and Italian bonds and it would not require a vote in Congress or Presidential approval. It would push the euro up against the dollar, but Europeans would not be in a position to complain. The People’s Bank of China is estimated to hold nearly 1 trillion euros already and it could switch them from German bonds to Spanish bonds.
In other words, rather than telling the Europeans to do some monetary stimulus, or attempting to force their hands with a currency war, the US or China could simply pump money into the European periphery. Normally, of course, if you're going to stimulate somewhere, you would rather it was your own country; but if you can stop a worldwide slump following the collapse of a massive currency bloc, that's a pretty good use of your time as well.
A recent ING analysis  (pdf) runs through six possible scenarios for the eurozone, including "Draghia" (where everyone gives in to Draghi, makes a banking union, and he does fiscal stimulus), "Inflationia" (sort of the Eurozone voluntarily doing what is described in point one) and "Bondia" (Europe introduces "eurobonds", all the countries pooling their costs of borrowing).
But if we're looking at unlikely solutions, then their sixth scenario, "Krugmania", fits the bill. It calls for lots of fiscal stimulus, mainly used for public investment, and the ECB not raising interest rates every time inflation peaks. If matched with a commitment to reducing deficits over the long term only, ING see this plan adding 3 per cent to GDP and 2 per cent to employment throughout the eurozone over the next two years.
4. Greece defaults but doesn't exit
John Cochrane, a professor at the University of Chicago, is annoyed  that Greece defaulting on its debt is always spoken of in conjunction with a Grexit:
The two steps are completely separate. If Illinois defaults on its bonds, it does not have to leave the dollar zone -- and it would be an obvious disaster for it to do so.
It is precisely the doublespeak confusion of sovereign default with breaking up a currency union which is causing a lot of the run.
But the main reason why default is spoken of is that doing so allows Grexit, which allows devaluation and a recovery in exports. Cochrane suggests that it be viewed another way:
They need to say they will tolerate sovereign default, bank failures, and drastic cuts in government payments rather than breakup.
Yes, cuts. The question for Greece is not whether it will cut payments. Stimulus is off the table, unless the Germans feel like paying for it, which they don't. The question for Greece is whether, having promised 10 euros, it will pay 10 devalued drachmas or 5 actual euros. The supposed benefit of euro exit and swift devaluation is the belief that people will be fooled that the 10 Drachmas are not a "cut" like the 5 euros would be. Good luck with that.
In other words, rather than defaulting in order to exit, default in order to avoid the exit. In this scenario, Greece is a sort of sacrificial lamb; they're damned if they do, or damned if they don't, but the rest of the eurozone is only damned one way. If they take the cuts and stay in the currency, maybe Spain and Portugal can be saved, at least.
5. Pan-european austerity
Actually, maybe not . Yeah, probably wouldn't work.  No, not even for Estonia , despite  what the President says . Especially given the "there's no money left" argument  doesn't really work when people are paying Germany to take their euros .