Shot, Reverse Shot

A common method of shooting dialogue: repeated Over the Shoulder shots interrupted by the occasional Medium Two-Shot.

This technique is often employed as a method of convenience; if it's impossible to get both of the actors together to film a shot, Over the Shoulder can be used with stand-ins who look, from behind, similar to the absent actor to complete the scene.

This is a standard technique from the Golden Age of Hollywood.

Examples of Shot, Reverse Shot include:

Film - Live-Action

Pick a major-studio film from the era before Cinemascope. Any of them.
Movie example: The initial conversation between Charles Xavier and Eric Lensherr in X-Men.
The prevalence of this approach in '30s-'40s Film Noir movies made it possible for Steve Martin to "act" with Bette Davis, Humphrey Bogart, Charles Laughton, etc. in Dead Men Don't Wear Plaid.
Used during almost every dialogue scene in the Star Wars prequel trilogy.

Live-Action TV

Any scene that involved both twins interacting in The Patty Duke Show.
The episode "Lie to Me" from the second season of Buffy the Vampire Slayer features this ad nauseam in the outside-the-school discussion between Buffy and Ford.
- Angel's appearance in the series finale was filmed that way because David Boreanaz was only available for a short time.
- There was a Buffy/Giles graveyard scene which used Sarah Michelle Gellar's stunt double accompanied by looped lines for the shots that were over Buffy's shoulder.
Michael and Hurley's conversation in season 6 of Lost were filmed this way, presumably because they only had Harold Perrineau for a short time.
The field interviews in The Daily Show with Jon Stewart are usually filmed this way.
Any given episode of the original Dragnet TV series with Jack Webb.
Examined by Charlie Brooker on Screenwipe, where he showed how much Manipulative Editing can be accomplished by interposing otherwise pointless shots of the interviewer nodding to cover the edits in the subject's answers.
Veronica Mars had to improvise an exchange between Veronica and a musician when the actor playing the musician couldn't come in to re-do the take. They hashed together the version where they were together with the one where Kristen Bell was delivering her lines to no one.