Invisible Celebrity Guest

The characters of a TV show encounter a celebrity...who is offscreen at all times. They're pointed out at the other side of the room, referenced as having just left, something like that; or we see An Insert of a hand or an elbow or the edge of a back of a head, which could essentially belong to anyone. Basically, they couldn't get the star to appear, or the bit was too minor to bother, or they're doing a subversion of the typical Celebrity Star episode.

Less common in animation, where you can pretty much draw whoever you want and impersonate the voice.

Film

In Monkey Business, the Marx Brothers, stowed away on a cruise liner, need a way to sneak off. Zeppo reveals that he ran into Maurice Chevalier - and stole his passport. Cue each brother trying to pass himself off as Chevalier to an increasingly irate customs officer.

Literature

For obvious reasons this doesn't happen very often in books, but there is at least one example: in the Thursday Next book First Among Sequels the two chapters before a big meeting are filled with people discussing a rumor that Harry Potter may put in an appearance. Once the meeting starts, the first announcement is that Harry couldn't make it due to copyright issues.

Live Action TV

Seinfeld had at least two fake cameos, by Uma Thurman and John Kennedy Jr., not to mention the innumerable back-of-the-head 'appearances' by George Steinbrenner.
The Single Guy had an episode where Sam unearthed an old recording which, ridiculous and bad as it was, he thought was a lost Beatles track. At the end of the episode the tape was bought back by Paul McCartney himself—which is to say, a faceless man in the back of a car, doing a bad Paul McCartney impression.
In the Doctor Who special The End of Time, President Obama is shown giving a speech, but only the back of his head is shown. Then he turns into the Master.
In Just Shoot Me!, Maya and Finch attend a party where Robert DeNiro spills a drink on Maya and Finch gets his photo taken with Madonna, yet strangely enough the only people we see there are total nobodies.
The pilot of Angel has Cordelia pointing out celebrities in a party—none of whom are seen.
On Mad About You Paul gets magician David Copperfield's suit by mistake. He later returns it to him—or rather, a stand-in seen only from behind.
Ex-president Gerald Ford's appearance on That '70s Show.
One episode of the short-lived live-action The Tick series featured Jimmy Carter. His face was never seen, though we did get to see the back of his head.
Being a famous popstar, Hannah Montana will frequently reference other celebrities that she knows. Most of them are never actually shown, but there have been exceptions.
How I Met Your Mother recently had a flashback to when the gang met Slash...who is never seen except for a glimpse of black hair and his Cool Hat.
Subverted in The Big Bang Theory. The guys are psyched that Stan Lee is coming to town. They talk constantly about him and his visit. Cut to us hearing about the aftermath of their experience with him. But then, during The Stinger, guess who makes an appearance?
Happened on a few episodes of The Golden Girls, most notably when then-President George H. W. Bush came to Miami and the ladies were chosen as the household he would actually visit. Each of the four women got to shake his hand through the open front door (his arm being the only part seen) while an impersonator provided his voice.
- Subverted on one episode where the ladies are set to attend a gala function and spend the entire episode talking about the celebrities who will be there. None of them are ever seen, because only Sophia gets to the party. But as the others are accusing her of making up everything she tells them about the event, Burt Reynolds shows up to invite Sophia for lunch.
On Murphy Brown Frank was going to be on Late Night with David Letterman but he got bumped. He came in to the studio and waved. They used the footage of actor Joe Regalbuto actually doing that from a time when he was bumped on the real Late Show, but just his shot with Dave saying "sorry" heard in the background. This was the first "appearance" of David Letterman on CBS very shortly after he had signed the contract to move his show there from NBC.
A long-running gag on the Mary Tyler Moore Show involved Mary's inability to throw a good party. In one late-season episode, she is promised an appearance by Johnny Carson at her latest party. After the usual run of disasters, the apartment plunges into total blackout - which is, of course, when Johnny Carson appears - or at least his voice!
In Community, Joe Biden is doing a tour of Colorado community colleges. Only the back of his head is ever seen.

Music

At the end of M.C. Hammer's "Too Legit to Quit" video, a producer turns to someone off-screen and asks what they think of the video. A white-gloved hand raises up and performs the hands signs for "Too legit to quit."

Radio

One notorious segment on the radio show I'm Sorry I Haven't A Clue had the host repeatedly mention that they had a celebrity guest, who would be playing Mornington Crescent with the rest of the panel. When the game in question rolled around, one of the regulars won on the first turn by saying "Mornington Crescent". For some reason, listeners accused the show of mistreating Alec Guinness, even though the "celebrity" never spoke and was never named (and likely didn't exist).

Western Animation

Foster's Home for Imaginary Friends had both Mel Gibson and Tom Hanks.... with buckets on their heads.
An episode of Bonkers dealt with a kidnapped Mickey Mouse, who spent the entire episode locked in a box and was referred to only as "the Mouse". This was especially unusual since we clearly hear his voice, and the show being produced by Disney seems to make this unnecessary.