In theory, anything can happen, and the world could end tomorrow. However, with a reasonably sane financial plan you should be able to ride this out.
If the government cannot or won't immediately pay its debt in full, the most immediate consequence is that people are going to be unwilling to lend any more money in future, except at very high rates to reflect the high risk of future default.
Presumably the government has got into this state by running a deficit (spending more than they collect in tax) and that is going to have to come to an abrupt end. That means: higher taxes, public service retrenchments and restrictions of service, perhaps cuts to social benefits, etc.
Countries that get into this state typically also have banks that have lent too much money to risky customers. So you should also expect to see some banks get into trouble, which may mean customers who have money on deposit will have trouble getting it back. In many cases governments will guarantee deposits, but perhaps only up to a particular ceiling like $100k.
It would be very possible to lose everything if you have speculative investments geared by substantial loans. If you have zero or moderate debt, your net wealth may decrease substantially (50%?) but there should be little prospect of it going to zero.
It is possible governments will simply confiscate your property, but I think in a first-world EU country this is fairly unlikely to happen to bank accounts, houses, shares, etc.
Typically, a default has led to a fall in the value of the country's currency. In the eurozone that is more complex because the same currency is used by countries that are doing fairly well, and because there is also turbulence in other major currency regions (JPY, USD and GBP). In some ways this makes the adjustment harder, because debts can't be inflated down.
All of this obviously causes a lot of economic turbulence so you can expect house prices to fall, share prices to gyrate, unemployment to rise. If you can afford it and come stomach the risk, it may turn out to be a good time to buy assets for the long term. If you're reasonably young the largest impact on you won't be losing your current savings, but rather the impact on your future job prospects from this adjustment period.
You never know, but I don't think the Weimar Republic wheelbarrows-of-banknotes situation is likely to recur; people are at least a bit smarter now and there is an inflation-targeting independent central bank.
I think gold can have some room in a portfolio, but now is not the time to make a sudden drastic move into it. Most middle class people cannot afford to have enough gold to support them for the rest of their life, though they may have enough for a rainy day or to act as a balancing component.
So what I would do to cope with this is: be well diversified, be sufficiently conservatively positioned that I would sleep at night, and beyond that just ride it out and try not to worry too much.
- Don't have all your cash savings in a single bank.
- Consider putting some money into a managed fund or ETF that invests outside of your country. This is easier to set up than a foreign bank account (ymmv) and diversifies against currency and local market risk.
- Live within your means.
- Keep your savings well diversified across location (home/abroad), asset class (cash/bonds/shares/property/gold), and institution.