Transformation of the Possessed

Being Demonically Possessed rarely works out well for the host, however, every once in a while It Gets Worse. Perhaps it's just that Evil Makes You Ugly, Evil Makes You Monstrous, or that your body is the plaything of the mind, but when the body your mother gave you has a new landlord there is a nasty tendency for you to be remodeled, and possibly shown off.

Sometimes justified in narration as the host becoming the new body of the guest either as a intrinsic feature or as a deliberate action on the part of the guest

Compare and Contrast: Glowing Eyes of Doom, Red Eyes, Take Warning, and Viral Transformation

Examples of Transformation of the Possessed include:

Anime and Manga

Apparently happens in Ao No Exorcist. Father Fujimoto is definitely an example. So is Toudou, later on, although it does seem to depend on how powerful the demon in question is.
Happens with Orochimaru's hosts in Naruto.
- when Naruto has a demon cloak with 4 or more tails the nine tailed fox is controlling him.
The 2003 anime version of Fullmetal Alchemist had Dante's deterioration with each possession.
Animals possessed by spirits in Berserk get deformed human-like faces
In Bleach, when Kaien is possessed by Metastasia he first gets hollowed, empty eyesockets, then he starts sprouting tentacles from his limbs, sockets and mouth.
In Soul Eater, when Medusa loses her body, she possesses a young girl and twists her appearance into a younger version of herself.

Film- Live Action

Legion: various angels do Odd things to the bodies they enhabit.
The Exorcist had a pretty gruesome transformation.
Happens twice in Constantine. In the beginning, when the soldier demon inhabits the young woman her face is covered with blotches. When Angela Dodson is possessed by Mammon (Lucifer's son) near the end the change is much greater. In each case, once the possession ends the skin changes disappear.

Literature

True for most Denarians in The Dresden Files, though some of them choose to keep their human appearance.
Played With in Perelandra, Dr. Weston's possessed body at first looks quite normal but as it is damaged beyond repair in the course of the plot (yet continues to move thanks to the devil inside it), it becomes horrible to look at and wholly inhuman.
In The Inheritance Cycle, when a human is possessed by spirits and becomes a Shade, it transforms their appearance, including turning their hair bright crimson.
Professor Quirell from Harry Potter and the Philosopher's Stone.
Spellbent: Possession victims get funky eye colors. Their sclera (white of the eyes) turns red or in some cases purple, depending on the power level of what's possessing them.

Live Action Television

In Star Trek: Deep Space Nine, when the Pa-Wraiths possess someone, the person's sclera's become red.
In Kamen Rider Den-O being possessed by any of the friendly—taro imagin gives the character a lock of appropriately colored hair and sometimes a change in wardrobe.
Demonic possessions eventually tend to disfigure the host in Buffy the Vampire Slayer and Angel.

Tabletop Games

Dungeons & Dragons 3.5 & 4.0: Many fiends find remodeling their new body to their advantage and extensive remodeling can result in being completely replaced.
In Warhammer 40,000, Daemons will alter the body of their host, moulding it into one more suitable for them. The host rarely lasts for very long.
In Demon: The Fallen, Demons knowledgeable in the lore of transformation can make permanent alterations to its host.
The Fomori in Werewolf: The Apocalypse. When a bane (an evil spirit of the Wyrm) possesses a human body, that person's body is hideously mutated with whatever the Storyteller picks from a grab-bag of disgusting Body Horror-based powers. Examples include multiple limbs and mouths, corrosive puss boils, and internal organs replaced by infectious fungus.

Video Games

Legacy of Kain: Raziel learns to occupy corpses and shape them into an image of himself
This happens to anyone possessed by a demon in Dragon Age.
In Diablo 2 this happens to the first game's protagonist when they fail to contain Diablo's soul.
When an Ing from Metroid Prime 2 fuses itself to a host, the host takes on a darker, mutated appearance as a direct result.
In Doom 3 (and, quite possibly, the old Doom games) demonic possession turns people into zombies.

Web Comics

Vaarsuvius from Order of the Stick takes on a demonic appearance after being Soul Spliced with three epic-level casters.

Western Animation

Jackie Chan Adventures: Shendu a dragon-demon-wizard wanted his current host Valmont to get scales. However, it was not a direct effect of the possession; he had to use potions for that.
After being possessed by Zordrak in an episode of The Dreamstone, Amberley gains a pair of extremely evil looking glowing eyes.