On July 2001 Comedy Central aired an episode of South Park named "Super Best Friends" that contained a depiction of Muhammad. The depiction was rather benign and not particularly satirical or insulting.
Given that this was the pre-9/11 world, not very surprisingly it went pretty much unnoticed and didn't cause much controversy at all.
On April 2010 Comedy central aired the first part of a two-part episode, named "200", that contained the same Muhammad characterization, except that it was (deliberately) censored so that the actual character isn't seen on screen (only a black censorship box). The double-episode is a social commentary on how the western world has been bullied into censoring all depictions of Muhammad. It makes no fun on Muhammad himself, but on the western fears. (The episode contains a lot of meta jokes about this censorship, as the characters themselves are not aware of the "censored" box, but it's referred to in the story at a meta level.)
After the episode had aired, a rather obscure Islamic organization issued a death threat to the authors, warning that if the second part was aired, there may be serious repercussions (among other things, they referenced directly the murder of Theo van Gogh.)
Comedy Central decided to censor the second part by bleeping out all appearances of the word "Muhammad", as well as the final speech (which was a satirical speech about how threat of violence is an effective tool to stop people from making satire). They expressed the sentiment that they weren't doing that lightly, but that they simply couldn't afford taking the risk of anybody getting killed.
This caused a rather huge controversy and debate over censorship, and how our free western society can be bullied into silence using intimidation and threats of violence (which, quite ironically, was the very point of the episode).
Many commentators wrote that this is exactly what we commonly express as "the terrorists win". This is exactly what terrorism seeks: Bullying people into submission using intimidation and threats. It's an affront to one of the core tenets of our free society: Freedom of expression. This is especially obnoxious because our western society gives Islam a special status over all other religions in this respect. (South Park has plenty of satire of all major religions, and none of it has caused actual credible death threats to the point of the distributors resorting to censorship.)
However, I would posit that what Comedy Central did was a lot better and useful than if they had simply ignored the threats.
If they had simply ignored the threats, the episode would have aired uncensored, and some religious organizations would have expressed their standard complaints, but overall it would have probably been a quite uneventful thing. Just one episode among others. Just typical South Park.
However, the very fact that Comedy Central resorted to censorship spawned the huge controversy in a manner that had actual relevance. It drew attention to the problem in a significantly more efficient way than the episode itself would have. Prominent commentators were actually talking about it, people all over the world were talking about it, it spawned the "Draw Muhammad Day"...
In the end, and somewhat ironically, I would say that Comedy Central's caving in and censoring the episode did significantly more good for our freedom of speech than if they had simply ignored the threats.
In other words, the threats had pretty much the exact opposite effect than the terrorists intended.