Social movements in the United States have had mixed results. Ones that you have heard of typically have ended up having decent results, but many others have not.
The most succesful social movement, I think, was the movement for black civil rights. This was very succesful in that it achieved all of its goals. It got the government to outlaw pretty much all forms of discrimination based on race.
But social movements don't always win. For example, you can say that there was a second part of the civil rights movement. Between the 1964 Civil Rights Act and his death in 1968, Martin Luther King, Jr. was working on a movement to try to improve the actual living conditions of blacks. He was trying to do things that would end de facto segregation and poverty, for example. He clearly failed in that and those problems continue to haunt the black community 40 years after his death.
I would recommend that you look at Piven and Cloward's "Poor People's Movements" for a discussion of why some movements do not work.