I get why writers and directors might want their names pulled from a project where they thought the finished work would not reflect well on them, or even just because they felt there was too little left of their contributions to warrant the credit. But I've never understod why actors would not want credit, especially when it's not a cameo, but something with at least a few lines, and they do a perfectly good job. This is one of the only two examples that I can think of off the top of my head (other being Delroy Lindo as the voodoo doctor in "Devil's Advocate" -- another great but underrated film IMHO). But I know there are plenty of others. Anyne got a clue?
Flickchick: This is sort of a complicated question, but here are the basics. First, movies made prior to 1960 list far fewer cast members than movies today, so many actors in small parts went uncredited as a matter of course. In 1960, members of the Screen Actors Guild went on strike to obtain residual payments for performers when films were sold to TV. Producers eventually agreed to pay residuals to all cast members listed in the end credits, and SAG negotiated credit for all actors with speaking roles, even if the role involves only a single line of dialogue. It should go without saying that actors are not penalized for playing mutes, like Samantha Morton's character in Sweet and Lowdown (1999).
Second, for performers in featured roles, billing (where and how his or her name appears) can be as important as money. Although there's some sheer vanity involved, salaries and billing for featured actors are negotiated on a film-by-film basis, and no one wants to set a precedent that could work against him or her in the future. Among the issues: Whether the actor's name appears before the movie's title or after; whether the name appears onscreen alone or with another name; of two above-the-title stars, whose name comes first; what size the name is compared to others; whether it's preceded by "and a special appearance by..." or encased in a box. This is negotiated by agents and producers, and occasionally causes a lot of trouble, sometimes as far back as the initial casting stage. You can't, for example, cast two stars in the same movie if both their contracts stipulate sole above-the-title billing. A good example of jockeying for billing taken to ridiculous extremes is the 1990 movie Havana, which stars Robert Redford and Raul Julia. Julia appears nowhere in the credits because of unresolved billing issues: Julia didn't want to be billed below Redford, and Redford wasn't budging.
A separate but related scenario involves a well-known actor taking a smaller-than-usual role, a situation that arose with Hannibal (2001). The small but pivotal role of Mason Verger, which required extensive prosthetic make-up, is played by English actor Gary Oldman. But he's not uncredited because his own mother wouldn't recognize him. Producer Martha De Laurentiis told Premiere: "He wanted a prominent credit. Now, how can you do a prominent credit... The [prominent] characters are Hannibal and Clarice Starling. So we really couldn't work something out [at first]." Oldman at first pulled out of the project, but later decided to go ahead and take no credit at all rather than a lesser one.
The case of Tom Cruise's credit in Magnolia is also illustrative. Magnolia is an ensemble picture, and mega-star Cruise's role is no larger than those of many lesser lights (luminosity in this case being judged by salary and position in the Hollywood power hierarchy). But Cruise wanted to work with director Paul Thomas Anderson, who wrote the flashy role especially for him. Anderson has said that Cruise planned not to take onscreen credit, but changed his mind when the film was finished and people began saying he had a shot at an Oscar nomination for his work. According to a spokesperson for the Academy of Motion Picture Arts and Sciences, an actor is not barred from nomination for an Oscar if he or she is uncredited — it's the performance that's being nominated, not the credit — although the situation has never actually arisen.
Dickering of this kind is, of course, the prerogative of well-known actors. If you're an aspiring thespian, you want the credit, even if it's "Ugly Bystander No. 3." When directors go uncredited, they use the pseudonym Alan Smithee. But that's another story.