Typically, you'd expect actors to be in the business of keeping themselves in work. If the trend of stars signing multi-picture deals and naturally gravitating towards the big franchises where the money is biggest and sequels most likely has taught us anything, it's that steady work is still a consideration for actors even when they hit the real big time.
So, it should come as something of a surprise that some actors have actually talked themselves out of more work. Whether because they didn't want to play the character any more or because they fundamentally believed that death was the only way their characters' arcs could develop, this morbid few literally demanded that they be killed off in major movies.
Whether they got their own way was sometimes a different matter though.
Sir Alec Guinness - Star Wars
Sir Alec Guinness' disdain for Star Wars has been well reported elsewhere already, but depending on who you believe, the acting legend might well have demanded his character be killed off because he thought the whole thing was terrible.
The reason it only qualifies as an honourable mention here is that George Lucas actually claims it was HIS decision to kill Obi Wan, because the character was no longer central to the plot after the Death Star escape. Apparently, this angered Guinnes so much he almost walked away, which is far removed from him demanding death come for him.