While actors most of the time fight over billing, there are times when they are not credited, either in the opening and advertising or at all.
Often this is because their role is a cameo, brief, often wordless, often done as a lark or a favour. It might be a speaking bit part or a silent "extra" appearance. Jack Nicholson had a tiny role as a news anchor in Broadcast News (presumably because writer-director James L. Brooks' earlier Terms of Endearment won him an Oscar).
Bing Crosby and Bob Hope were seen in the circus audience when their Road movie co-star Dorothy Lamour appeared in The Greatest Show on Earth. Tony Curtis provided a vocal cameo on the phone in Rosemary's Baby.
But it can happen even with more substantial roles. Sissy Spacek and James Earl Jones went uncredited for their vocal characterisations in The Man With Two Brains and Star Wars, respectively.
For Se73n, Kevin Spacey went unbilled in the advertising and opening credits to preserve the surprise (which has surely long passed) when he appeared. Gary Oldman was heavily made up to play the disfigured Mason Berger in Hannibal and declined billing for ghoulish amusement as he was playing a man with no face (or at least not much of one).
Gene Hackman, better known as a dramatic actor, used his friendship with co-writer and star Gene Wilder to land the role of the blind hermit in Young Frankenstein: his scene was a very funny highlight. But Hackman also declined billing for his substantial role in The Firm, reportedly because Tom Cruise was to be the sole name above the title. Hackman chose not to be billed rather than be relegated to below-the-title status. Cruise went the anonymous route for his heavily made-up comic turn in Tropic Thunder.
Don Cheadle, who appeared unbilled for fun in Rush Hour 2, refused credit on Ocean's Eleven, apparently because he was denied above-the-title billing alongside George Clooney, Brad Pitt and Matt Damon (he got it in the sequels).
While the internet is full of spoilers, keep your eyes and ears open and you might get a surrpise.