Since the Civil Rights Movement for black rights was far and away the most successful movement in the last century (the movement for women's votes took a lot longer to win its goals), it is not surprising that its methods influenced everything that has come after it.
Perhaps the most obvious influence is the use of sit-ins where the protestors attempt to force the police to arrest them. This has been used by movements that range from anti-abortion protestors to anti-nuclear protestors. The use of nonviolent civil disobedience has also had an effect on the ways in which most other protest groups have tried to get their messages across.
Another thing that the Civil Rights Movement did was to craft protests that would get media attention and thereby publicize the cause. This impacted other movements as well. You have/had things like women burning their bras, gay pride parades with people dressed (or not dressed) in very "out there" ways, and abortion protestors displaying pictures of aborted fetuses. All of these are meant to attract attention just as the marches of the Civil Rights Movement did.
I think this is a great question. I have been fascinated with this topic for so many years. Indeed, the Civil Rights Movement laid the fundamental groundwork for other movements that followed. Women's movements in the late 1960s and afterwards appealed to the social dynamic of being heard, borrowing language and syntax from the Civil Rights Movement. The placard which read, "I am a Man" from the 1950s marches throughout the South was appropriated by the Feminist movement and even through song with Helen Reddy's "I am Woman." The workers' plights were articulated by leaders like Cesar Chavez, whose hunger strikes and methods of protest were reminiscent of Dr. King. Finally, the notion of acceptance and tolerance, the idea of waiting too long and demanding entrance was a recurrent theme in Civil Rights action seen in the thoughts of Malcolm X and Kwame Ture. This very idea "came out" with the Gay Rights Activism of the late 1970s. The very idea of "out of the closet, into the street" is very reminiscent of the more active Civil Rights Activist. The issue of representation and the crisis in the lack of it, first discussed by African American thinkers in the Civil Rights Movements, became something that was brought out by other movements that followed.