I personally wouldn't turn to violence, but only because I'm not a physically aggressive person - in fact, I'm rather cowardly when it comes to conflict. I can understand why people would, though. The people of Greece have tried: Austerity. It didn't work. The economic situation declined further. Protesting the austerity package, peacefully and democratically, whilst retaining their government. It didn't work. The party accepted its debtees' demands for more austerity. Democratically and peacefully electing an anti-austerity party. It sort-of worked in that the party said "maybe, we'll have a referendum". Voting "No" to austerity, peacefully and democratically, in said referendum. It didn't work. The party accepted the terms of another austerity package.
It seems to me that the Greeks have been doing all they can through democratic and peaceful channels, and - however much sympathy for them the rest of the world may have - their demands have not been met.
There probably are other channels of participation, but I can't immediately think what they would be.
And I'm pretty sure if I can't think of them, the poor Greeks - after five years of poverty and high unemployment and not being listened to - aren't really in the mood to think of one either. I agree, daltonslaw, that violent protest doesn't solve anything. But I can understand where the frustration comes from, and I think the rest of Europe (myself included) shares the responsibility for the Greeks' plight.
The more I learn about this, the more I think the people of Greece have much to be angry about. Their government has sold them out too many times now. I can't even begin to understand how they must feel. I can't imagine this happening here in America.
No, I can't really imagine it happening in America either, particularly not at the national level. But the role Greece has in Europe is not quite like the role America has in the world.
A good way of thinking about the power structure might be to equate Greece with a state (say, Maine) and the Brussels government with Washington. Now say Maine decided it wanted to introduce lots of public services - brand new schools, public healthcare, free higher education, stuff like that, and borrowed money to do so, and it got to borrow money cheaply because it was part of the US. And then, ten years later, Maine was suddenly like "I totally can't pay all this back, sorry. I guess I'll just declare myself bankrupt. It worked for Argentina..."
In that case, I could envisage Washington stepping in and obliging Maine to sort out its finances. Especially once all the big banks Maine owed money to started lobbying. And however much the people of Maine complained about having all their public financing cut, I doubt the state would have much leverage.
It's not the same, of course, as Greece. Greece's spending, though prolific, was in line with European norms (Free universal education and healthcare etc. are pretty much considered a basic human right in Europe). Greece is an independent country, not a state. But. It did benefit from being in the Euro, then mess up its finances and jeopardize that very same currency union. None of this, of course, was the fault of your average Greek person, hence the unfairness of it all. And the irony, of course, that all this happened in the country that invented democracy.