1950s. USA. Paul Robeson
In the 1950s, musicians as well as the denizens of Hollywood felt the force of the McCarthyite witchhunts and the House Committee on Un-American Activities. No-one more so than Paul Robeson.
According to Julian Petley's article in Index of Censorship in 1998, Paul Robeson is "undoubtedly the most censored of all American musicians." After years of harassment and vilification, the State Department revoked Robeson's passport in 1950, and US officials prevented him from singing in Canada in 1952. He was subpoenaed by the House Committee in 1956.
Source: Index of Censorship: ‘Smashed Hits’ Volume 27, 6/1998, p. 15.

Febuary 1952. USA. Seeger & the Weavers
The Weavers had major hits in the early 1950s. The song ‘Wimoweh’ was recorded in 1951 by Pete Seeger and his band The Weavers, in a version faithful to the Zulu original. But this was the era of McCarthy witch hunts in America, and Pete Seeger's politics made him an inevitable quarry of the commie-chasing House Un-American Affairs Committee. Just as ‘Wimoweh’ made its chart debut, a former trade union colleague of Seeger's named Harvey Matusow denounced the musician to the committee. In "one of the looniest tales of the entire McCarthy era", Harvey Matusow testified that communists were "preying on the sexual weakness of American youth". And he was willing to give names – one of which was Pete Seeger. The public reaction was immediate. The press went wild, Weavers' shows and television appearances were cancelled, radio stations banned their records and ‘Wimoweh’ tumbled off the charts. This was in February 1952. 
On August 18, 1955, Pete was subpoenaed to testify before the House Un-American Activities Committee (HUAC) where he refused to name personal and political associations stating it would violate his First Amendment rights.
"I am not going to answer any questions as to my association, my philosophical or religious beliefs or my political beliefs, or how I voted in any election, or any of these private affairs. I think these are very improper questions for any American to be asked, especially under such compulsion as this," he said.
Seeger's refusal to testify led to a March 26, 1957 indictment for contempt of Congress; for some years, he had to keep the federal government apprised of where he was going any time he left the Southern District of New York. He was convicted in a jury trial in March 1961, and sentenced to a year in jail, but in May 1962 an appeals court ruled the indictment to be flawed and overturned his conviction.
Pete Seeger did not appear on television for 17 years, until the Smothers Brothers broke the boycott.
Source: http://en.wikipedia.org/wiki/Pete_seeger and others.

1955. USA. 'Black music'
15,000 letters, mostly written by young adults, are sent to Chicago rock stations accusing them of playing "dirty" records. Radio station WABB runs editorials called ‘About The Music You Won't Hear on WABB’. The editorials promise that the station will censor itself of all controversial music, especially rhythm and blues – in other words, "black" music.

1958-1959. USA. Link Wray
Link Wray’s convention-shattering rock instrumental 'Rumble' ands in the U.S. Top 20 despite being banned in several radio markets for its violent evocations – even though it has no lyrics. The title of the song is thought to be suggestive of teenage gang violence. When Wray performs on American Bandstand, Dick Clark introduces him but doesn't say the title of the song. Three-quarters Shawnee Indian, prolific Link Wray was later named by Rolling Stone as one of the 100 greatest guitarists of all time.
Source: www.linkwraylegend.com