Flip Personality

They've caught a Body Snatcher or Symbiote, or are Sharing a Body, and you can tell, because they're obviously switching between minds repeatedly. Often accompanied by changes in manner, posture, voice, or eye color. Those not aware of the circumstances and not sufficiently well acquainted with the originally one-minded character may not notice the change, leading to much opportunity for hilarity to ensue.

Having arguments with yourself is strictly optional, but again, hilarious.

Anime and Manga

 * In Black Butler II, and both souls dispute its control. You can see — quite easily —  is in charge because of the (not subtle) change in attitude and because the eye seal disappears.
 * Taken to extremes with Launch in Dragon Ball, whose body undergoes a physical change when she switches personalities.

Literature

 * Demons in Paladin of Souls. Those with second sight can see who is in control of a body.
 * Altogether Andrews from Discworld, first introduced in The Truth.
 * Also Agnes Nitt and her alternate personality, Perdita. No physical change, but the personality change is very, very distinct.
 * In Black Star Rising by Frederick Pohl, there's a Chinese scientist who's had his damaged brain augmented with bits and pieces from other people's brains. Some of their memories and personality traits came along. Despite the nightmarish concept, he seems to be fairly indulgent of the desires of his "donor" personalities, as shown when he asks to meet one of the main characters, because the mother of the other fellow's wife was one of those donors. "Well, I'm her mother!" He's nicknamed "Manyface," because of the way his expression changes as different mind-portions become dominant from moment to moment.

Live-Action TV

 * Toby in the Doctor Who episode "The Satan Pit". When he's possessed, his eyes turn red, his body is covered in arcane writing, and he shouts imprecations in a gravelly voice. It turns out, however, that the times when he appears and acts normally are actually a ruse.
 * The Stargate Verse has several examples:
 * The Tok'ra symbiotes and their hosts from Stargate SG-1. The symbiote taking control is revealed by an altered voice and temporarily glowing eyes.
 * In the SG-1 episode "Lifeboat", a quite large number of consciousnesses get downloaded into Daniel, and he sort of cycles through them.
 * In the Stargate Atlantis episode "Duet", Cadman and McKay share a body as the result of an accident with a Wraith transporter beam, and spend some time fighting over it.
 * Stargate Universe: Episode "Hope". Two more consciousnesses got uploaded into Chloe's mind.
 * There's a Star Trek: Deep Space Nine episode where other characters voluntarily share their bodies with the personalities of previous Dax hosts. Quark is very uncomfortable with the personality he's hosting and keeps emerging to complain.

Video Games

 * One of the gods in Eternal Darkness has two personalities that act like this.
 * In MARDEK, The Hero shares his body with the soul of an alien mage called Rohoph. You can tell instantly when Rohoph is talking because Mardek's eyes glow white and his speech pattern (and font) changes completely.
 * There's also Legion, a robot animated by dark magic and containing four different souls. One's an Evil Overlord, one's completely insane, one's a mopey, depressed guy named Marv- er, Martin, and the last one, a shaman, is the Only Sane Man. Their text color changes depending on which one's in control at the moment.

Web Comics

 * Lucrezia and in Girl Genius. No outward signs of transition, but obviously different personalities.

Web Original

 * In Red vs. Blue, when O'Malley possesses Doc, their body frequently switches personality on a sentence by sentence basis, this is shown by voice and mannerism changes and camera angle changes. The two characters actually hold conversations with each other, or will cut in on what the other is saying to make some kind of wise-crack or amendment. For the most part O'Malley is in control of what they do, however. All the characters are pretty much aware of this as well, and since it's a comedy no one really cares except when O'Malley is trying to kill them and take over the world.