In some ways, this isn't a great plan. It punishes those who saved their money while rewarding those who consumed their income. It also means that people will have to start assuming that wealth taxes on bank account balances may happen in more jurisdictions and that they should move their money into what they deem to be safe jurisdictions. This could do harm to other countries whose banking systems have been having trouble.
This is not some sort of illegal seizure - and wouldn't even be in the United States. While we normally tax income or consumption, governments can and do tax wealth. In the United States, property taxes are quite normal. What is the difference between charging someone x% of their house value in taxes and charging someone x% of their bank account balance in taxes? It's mostly normative: we're used to taxes on physical property like houses, but not used to taxes on cash that we carry in banks. If the government decided tomorrow to switch from property taxes to bank account taxes, would you care? Mostly, it would depend on where the bulk of your wealth is. If it were in your home, you would welcome the change.
I think the reason that they chose to go after the bank balances is that a lot of it is foreign-owned. In many ways, this is much better for the Cypriot people. They may not like seeing their bank accounts go down by 6-10%, but this method spreads the burden to a lot of foreigners. If they went the route of imposing a high property tax, they would have to shoulder a much higher burden.
It's also easier to implement, in a certain light. If you impose a new tax of, say, 2% on the value of real property holdings, people are going to lose their houses when they can't come up with the money for the tax. You don't want that: it would just be chaos. Taxing the bank accounts is taxing a liquid asset. You know they have the cash to cover 10% of their bank account balance because, well, it's their bank account balance.
Since they're going to impose the levy before the banks open on tuesday (monday being a banking holiday) and banks putting a withdrawal limit of 400 Euros on customers, it looks like it can be implemented.
In many ways, it's the easiest, quickest successful tax that they could impose. And, while it will cause a lot of uproar from Cypriots, it's probably better than any other measure for them. If the government were to try and raise the money from other means (whether a real property tax, higher consumption taxes, higher income taxes, etc.), the burden would fall on residents more than this tax will. Similarly, this tax will hit the rich harder than the poor. If they raised VAT, income tax, or real property tax, the rich could move elsewhere and be spared a lot of it.
EDIT: I'm going to respond to some replies here.
First, I never said this was a good plan. I said that it would be easy and quick from an administrative standpoint. The ECB doesn't seem to want something long and drawn out or get into a situation where legislative processes and elections throw everything into chaos. Since Cyprus wants the bailout, the ECB holds a lot of the cards. We've seen how governmental changes can throw a wrench into the bailout agreements. Because this levy can be implemented "overnight", it's easy and doesn't rely on a legislature agreeing on austerity measures for many years.
This solution will be a betrayal of people's trust, it will hurt people. It will make people think twice about putting their money in banks. In fact, this is something that parts of Latin America face. However, are there alternatives for coming up with 5.8 billion Euro that would be better?
Frankly, in order to criticize well, you have to bring up other solutions against the chosen solution. This move is bad. No one thinks this is a happy move. It has cons. People will lose savings (including money they were counting on having). People will distrust banks for the foreseeable future. It will create resentment and anger. It will be bad. So, what would be better?
Now, one can argue that defaulting on the debt would be better - that's certainly a position to take. However, assuming that Cyprus doesn't want to default, how else should they have secured the ECB bailout (assuming that one needs to raise 5.8 billion Euro to do so)?