Basically the problem appears to be that Greece can't might default and if it does that will create problems for the rest of us as a lot of Greek debt is held by banks in a lot of countries.
The solution is basically to merge all the debt into a central fund managed by the ECB and give the ECB/European Parliament powers to set upper and lower bounds for spending and taxation respectively. The latter part would be necessary in order to prevent one member just borrowing lots and passing the cost onto the other members. This would also allow some of the poorer members to be allowed deficits funded by the issuing of "Euro-bonds" or through the surpluses of the richer members.The Eurozone as a whole would be in a decent position to service its debt, but at the moment the entire thing is at risk because of one member.
Now firstly I should mention that I'm not a fan of the Euro, I do not support the UK joining it, but if there is going to be a single currency then there needs to be some degree of fiscal union for it to be stable. The Eurozone must either go forwards or backwards, it cannot remain where it is. To use a metaphor, they are standing in the middle of a bridge during a gale, they should either go back to where they came from (as in return to their own currencies) or go to the other side (as in enter a fiscal union).
So there, a solution to the problem. You're welcome world, I'll await my medal.