No American bank is really sound, and were it not for the Fed and the FDIC, the banksters' folly would lead to perpetual bankruns (which is why we need a gold standard and 100% reserve banking for a free and sound economy).
But some are more bankrupt than others, and clearly some are tottering on the edge. Will they tip over this time, after two decades of Greenspanite mania?
It's not a good sign that the biggest of the big banks--Deutsche Bank, Citigroup, Bank of America, Wachovia, J.P Morgan-Chase, etc.--are borrowing at the discount window. That is, they are getting newly created money at a premium to keep them in existence hour to hour.
It may seem as if the Fed can print unlimited dollars, but then it faces hyperinflation and the collapse of the already-sliding dollar internationally, and perhaps the end of the dollar-reserve standard, and therefore the empire. (Not to speak of the destruction of dollar assets here at home.)
We live in interesting times, thanks to the monsters who gave us the central bank. But monetary reform is possible, perhaps before a catastrophe. See this video.