Government insurance means nothing when the government is broke (relative to the size of its banks). Nicosia does not have the €30 billion to reimburse accounts covered by the country’s deposit guarantee scheme. No bail-out means depositors being wiped out.
The Cypriot banks are going to find all of their deposits withdrawn as soon as they reopen, so they better figure out a new way to finance themselves.
In a theoretical free market, depositors would lose all their money if a bank goes bust, just as stock holders lose their money if a company goes bust.
Banks, however, hold a particular role in a modern economy that regular companies don't. As such, deposit insurance is a necessity for overall financial stability. In the case at hand, the decision by the Cypriot gov't to effectively cancel deposit insurance for smaller depositors is their biggest mistake, since it decreases confidence in both the banks and the gov't.
It's hard to really get your head around how wrong headed this decision is.