Most genre shows have the occasional format-bender and sometimes a total format-breaker. Doctor Who has such a flexible format that it can bend quite easily to contain fourth wall breakers, locked room dramas, live stage appearances, cartoons, out-and-out horror, out-and-out comedy, episodes almost entirely lacking the main characters...
The trick with a Format-Bender is to still provide a fun evening's viewing or gaming, so grab something you know your players would be interested in.
Since these are all as different from each other as from the more common story types, I won't try and delineate common features except in the latter case, but instead offer some examples.
9: They'll talk about this for years to come...
Breaking The Fourth Wall
This is most literally the cast looking at the camera and addressing the audience, but can also involve other metafictional ideas. Doctor Who is such a huge chunk of British pop culture that the Whoniverse not having Doctor Who in it is almost as strange as it having aliens attack London every Christmas. How would the Doctor react to seeing a display of Doctor Who toys at Hamleys? (By way of example, scroll down to TV ACTION!)
A less extreme example can be found in Love and Monsters, which was also a Doctor-Lite Episode. It takes the idea of video diaries, found footage and straight-to-camera reality TV and runs with it. This almost happened again in Series Four, with an episode where the Doctor crashed the filming of Most Haunted. They're talking to us directly, but still in the normal universe of the show.
Similarly, a classic SF conceit is to take the characters to a different reality, possibly created by a time paradox or some other effect, where the "normal" setting is dramatically different, and see how they escape or fix the changes. This lets you wreak havoc with the setting, change NPCs drastically, let the PCs meet their parallel selves and more. Bonus point if the Brigadier has an eyepatch.
A relatively normal adventure based on an even stranger premise than usual. Like the 2010 Doctor Who Storybook had a story about a Secret Invasion being organised by psychic entities in the forms of doors.
I'm Missing Something...
A relatively normal adventure but with something wrong. Like one of the Companions is gone, or there's a new one, and nobody seems to have noticed this wasn't the case last week. A very sly way of covering an absent player's character, if you have enough warning that the player's going to miss a session.
Or the adventure starts halfway through and the players have to piece together what just happened because the characters' memories of the last few days have been wiped. For this, you'd need a fair idea of how the PCs would react to the events that they missed.
There's rather a lot of borrowing and homaging in Doctor Who already, but specifically here it's for laughs and/or satirical points. An obvious way to bring this to the gaming table would be to have the TARDIS crash into another game's setting. Need an example? Here's about thirty. Including an actual Who serial.