Here are some of the ways in which censorship can be dealt with:
- Blanking; when the volume is muted for all or part of the word.
- Bleeping; playing a noise, usually a "beep", over all or part of the word.
- Resampling; using a like-sounding portion of vocals and music to override the offending word.
- Backmasking; taking the offending word and reversing the audio, sometimes the whole audio is reversed (often because it is a home-made job), but more usually only the vocal track is reversed.
- Repeating; repeating the word just said before the explicit word was used.
- Skipping; deleting the word from the song without a time delay.
- Echo; instead of saying a word, it echoes the last word(s) said in the line.
- Disc scratching; in hip hop, scratching on the word, making it sound like another word, or make the word said faster or slower.
- RoboVoicing; making the word totally non-understandable by overpowering a robovoice effect (usually used as a last resort for home-made jobs).
- Distorting; Usually in Hip-Hop, less offensive words such as "shit" or else is distorted. It is usually done by shifting down the pitch.
Examples of artists who have had their work edited or censored:
Fela Kuti, Nigeria - Imprisoned and harassed by Nigerian authorities
Ferhat Tunc, Turkey - Censored and imprisoned by Turkish authorities
Gorki Águila, Cuba - Censored by the Cuban Government. Imprisoned August 2003 
Judge Dread, England - The Guinness Book of World Records credits Judge Dread for having the most banned songs of all time on the BBC Radio.
Madonna, USA - Several videos banned and attempted boycott (usually by religious groups) of several of her concerts (such as her visits in 1990 and 2006 to Rome, her visit in 2006 to Russia, her visits in 2009 to Poland and Bulgaria, etc.). When American television network NBC aired a concert from the artist's Confessions Tour, the part of the show where Madonna stages a crucifixion was censored and replaced with images of orphaned African children (images that were part of the live performance involving the crucifixion, but which were displayed on the on-stage screens behind the singer).
Marilyn Manson, USA- His release of "(s)AINT" is banned in many countries due to its content including BDSM, cunnilingus and drug use along with masturbation.
Miguel Angel Estrella, Argentina - Banned, imprisoned and tortured by the Argentine military junta 
Matoub Lounès, Algeria - Assassinated in 1998
Thomas Mapfumo, Zimbabwe - Several songs banned by Zimbabwean authorities
Most of the information found on Wikipedia
Robbie Williams only has one censored video, this being Rock DJ. The video showed Williams in an attempt to get noticed by a group of females, first stripping and then tearing chunks of skin and muscle from his body, and caused controversy in the United Kingdom and many other countries. The video was edited by Top of the Pops for its graphic content and many other channels followed suit.