Here are some bigger ones:

The Civil Rights movement that put a stop to official, written-into-law segregation in the 1950's and 1960's. Yes, I am talking about Martin Luther King, the Freedom Riders, and those who faced down Bull Connor's dogs and firehoses.

Twenty years later, there was a huge civil disobedience campaign in the United States to demand an end to investments in South Africa during the apartheid era. This campaign contributed to the end of apartheid but did not stop it alone.

Over 100,000 people left the U$ for Canada and elsewhere after refusing induction into or deserting from the Armed forces during Vietnam.Refusing to show up after being drafted is a form of civil disobedience, and desertion sure as HELL is.

Oh and by the way, let's NEVER, EVER forget how whole tribes and bands within tribes refused to be frog-marched onto reservations after things like Andrew Jackson's Indian Removal Act. Since half the Cherokee Nation refused to be "removed" until guns were held to their heads but did not use armed force themselves, I believe that constitutes civil disobediance.

Personally, I prefer the approach of Geronimo, Tecumseh, Sitting Bill, and Crazy Horse, but it was up to the Cherokee Nation to choose their own strategy. The Cherokee chose civil disobedience, and surely were larger than the number of Americans doing civil disobedience today over the Iraq War!