Silent Conversation

The audience (and usually third party) is observing a conversation between two characters, but no audio can be heard.

The actual content of that conversation remains a mystery to the audience except partial excerpts or references made by the parties who were there at the time. Though sometimes they are revealed entirely in a Flash Back at the end.

This will cause a lot of head-scratching and fanfics if the audience doesn't just go along with it.

Anime

 * Irresponsible Captain Tylor has plenty of these: Harumi, Yuriko,  and Admiral Hanner in the OAV mini-series An Exceptional Episode.

Live Action TV

 * The Mentalist has one between Bosco and Jane. Afterward, Lisbon wants to know what Bosco told Jane, who only hints that Bosco wanted him to protect her.
 * In an episode of Seinfeld, George confronts a coworker over stealing an office nickname that he wanted. The conversation is watched by other coworkers through a window, while George waves his arms around and apparently yells at the guy. When the audience can hear the two again, he lets George have the nickname and asks him to stop crying.
 * Doctor Who, "Logopolis": The Doctor has a somber conversation with the Watcher, a mysterious, featureless being. We see it from the companion's perspective, across the freeway. (We never learn exactly what they talked about, but later we learn who the Watcher is.)
 * The UK Office: Tim turns his mike off (it's a mockumentary) and goes to talk to Lucy. A very powerful use of this trope: we see them from the other side of a window, we hear dead silence, for 2 minutes. Afterwards, he says:
 * Buffy the Vampire Slayer: In the episode "Showtime" there's a scene in which Buffy, Willow, and Xander all exchange some meaningful looks without saying anything. A flashback at the end shows that they were having a telepathic conversation, setting up the plan for the rest of the episode.

Newspaper Comics

 * In a Peanuts Sunday strip from the 1960s, Charlie Brown gets a phone call for Snoopy. During the call, Snoopy listens and laughs, but Charlie Brown doesn't know what the caller is saying.