Today, how likely is a run on US banks?

Question posed to the knowledgeable economists out there: Are we on the brink of another depression, economically speaking? Should I withdraw the money I have in the bank? If there's a run, will I be able to access my money? Aside from the highly-publicized bailouts that led to runs, what are the signs to look for that signal a run is about to happen? Anything? Serious, knowledgeable replies only please.