Demonstrations from New York to Seattle were mostly peaceful but rioting broke out in Oakland, California.
There was some unrest in Ferguson itself, with police making 44 arrests, but the town did not see rioting on the scale of Monday night.
The officer who killed Michael Brown there says he has a “clean conscience”.
Darren Wilson, who shot the 18-year-old on 9 August, told ABC News that in the struggle which preceded the shooting, he had felt “like a five-year-old holding on to [US wrestler] Hulk Hogan”.
Officer Darren Wilson, who shot and killed Michael Brown: “I know I did my job right”
Many in Ferguson’s predominantly African-American community had called for the officer to be charged with murder, but the grand jury’s decision means the police officer will not face state criminal charges over the shooting.
Lawyers for Mr Brown’s family denounced the grand jury’s decision as “unfair” while condemning the violence that followed the decision.