The best-known example was the saga of DDR Dave Thomas. Posted on Newgrounds on January 4, 2002, Wendy's founder Dave Thomas died four days later, January 8. This immediately led to speculation of a curse.
There are no explanations as to why the curse would only affect certain characters, mainly ones who were only used in one or two movies. Major examples include Matthew Lesko, Colin Mochrie, and Alex Chiu. Earlier, people had suggested that Dave Thomas actually saw the movie, which caused his death. However, now that it is known that Lesko and Mochrie both know about their animutation star status, an inverse theory might hold up better: that animutation characters can fall victim to the curse if they don't see movies featuring themselves. It is unknown whether Alex Chiu has seen any of the movies featuring him, such as We Drink Ritalin, but he invented the Immortality Rings, which could be another cause for his immunity.
Another form of The Curse was brought up by KKyuubi in relation to his movie Power 50, which showed a newscast (anchored by Cosmo Kramer) airing on Chicago's owned and operated ABC affiliate WLS-TV in High Definition (according to the aspect ratio of the movie, and the "07-HD" display when the channel switched). At the time, WLS-TV did not air ABC7 News in HD, but on December 14th, they announced plans to go HD on January 6th of 2007. The curse in this way, made it so that the real life form of WLS would end up being presented in the same way that it was shown in the movie (HD). In this case, how something happened in an animutation, ended up happening in real life too.
It was briefly referenced to in Hyakugojyuuichi Forever. When Dave Thomas pops up, his pacemaker explodes and he says, "Ack! I'm a Fanimutation!"
On another note, although not animutations, Andrew Kepple's Up Skit Creek series featured Pope John Paul II in the first, Steve Irwin in the second, and Samuel L. Jackson in the third. The first two died within a year of their respective appearances, but what fate belies Samuel L. Jackson is yet uncertain.