On contrary of what Mike Scott suggested, I think in case of EURO DOOM it's a lot safer if your savings were changed into another currency in advance.
Beware that bringing your money into an EURO CORE country (like Finland, Austria, Germany, Nethereland) it's useful if you think those banks are safer, but totally useless to avoid the conversion of your saving from Euro into your national currency.
In case of EURO CRASH, only the Central Bank will decide what happens to ALL the Euro deposited wherever, single banks, even if they are Deutsche Bank or BNP or ING, can not decide what to do on their own.
ECB (European Central Bank) might decide to convert EURO into local currencies based on the account's owner nationality. Therefor if you are Greek and you moved your saving in a German bank, the ECB might decide that your Euro are converted into New Dracma even if they sit in a German bank account.
The funniest thing is that if you ask to a Finland bank: "In case of Euro crash, would you convert my Euro into New Dracma?", they sure would answer "No, we can't!", which is true, they can not because it's only the ECB (Europe Central Bank) the one that decides how an ordered Euro crash has to be manged, and the ECB might decide as I explained you above.
Other Central Banks (Swiss, FED, etc.) would only follow the decisions of the ECB.
Moreover in case of EURO DOOM, it's highly probable that the Euro currency looses a tremendous value compared to other currencies, the loss would be huge in case the Euro Crash happens in a disordered way (i.e. a strong country like Germany and their banks decides to get out and they start printing their own money w/o listening to the ECB anymore). So even if your saving are in Euro in Germany they would loose so much value (compared to other currencies) that you will regreat forever not to have converted them into another currency when you had the time to do it.
Couple of advises:
1) If you want to change you savings into another currency you don't need to bring them into another bank/country (like US), you could simply buy US Shares/Bonds at your local bank.
Shares/Bonds of a US company/US gov will always be worth their value in dollars no matter in what new pathetic currency your account will be converted.
2) But is there a drawback in converting my saving into another currency (i.e. buying dollars in the form of US treasury bonds)? Unfortunately yes, the drawback is that in case this Euro drama comes finally to an happy ending and Germans decide to open their wallets for the nth time to save the currency, the Euro might suddenly increase its value compared to other currencies, therefor if you changed your saving into another currency you might loose money (i.e. US dollars looses value against the Euro).