When Naruto has a demon cloak with four or more tails, the nine-tailed fox is controlling him.
The Edo Tensei technique works by taking some genetic material of a deceased person and forcing them into a still-living body. This transforms the host's body into that of the deceased person's, killing the host in the process but allowing the body to become animate.
In Chapter 679, Kaguya apparently inflicts this on Madara.
Judge Dredd: The Dark Judges tend to possess people solely to asssist them in finding new corpses for their spirits to occupy after the destruction of the previous one, but Judge Mortis once possessed the Chief Judge and directly decayed his body into the cow-skulled monster that he is.
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.
Legion: various angels do odd things to the bodies they inhabit.
The Devil Inside plays it straight, but in fairly plausible ways. Those possessed sport freakish flexibility, dilated eyes (a line of dialogue indicates that the human eye can dilate to 9 mm, 11 mm under the influence of some drugs, but possession can force it further), and red eyes. All could be explained by actual physical symptoms.
The Candarian demons in the Evil Dead series use this in a variety of ways.
In the original film the only change was in the eyes (and spreading black veins in one case), but physical damage inflicted on the host quickly reached gruesome levels.
Evil Dead 2 had a greater degree of Body Horror, including a possession victim with an extremely long neck.
Army of Darkness had Sheila suffer some minor changes in bone structure when she was possessed, and the rest of the Deadites took on a rotted appearance even without any injuries.
Finally, the 2013 remake only gives the possessed yellow eyes by default, but they then inflict gruesome injuries on themselves, apparently to match the documented appearance of whatever spirit is possessing them.
Happens to the Chosen One in John Carpenter's Prince of Darkness. Satan, in the form of an evil green fluid, enters the mouths of his victims to control them, but the Chosen One ingests the lion's share of the fluid and becomes the personal vehicle of Satan himself. (This causes said Chosen One's body to appear progressively rotten and decayed as the movie goes on.)
In Demon Knight, this is the fate of everyone possessed by demons. The last transformation in the film of a young boy is especially grotesque.
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 Inheritance Cycle, when a human is possessed by spirits and becomes a Shade, it transforms their appearance, including turning their hair bright crimson.
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 Warhammer40000, 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.
Likewise, the spirits in Werewolf: The Forsaken can do this to their hosts, but only at the point where they've either destroyed the host's consciousness or irreversibly taken over their soul. In any case, the body starts to take on elements of the spirit possessing it - for the Hosts, this is usually the creature the Host derives from (examples include spiders, rats, crows, worms, fungi, etc.), but for the Spirit-Claimed, the possessed takes on elements of its nature (a fire elemental will give its host bright eyes and blisters, a death spirit will make its host look gaunt, etc.).
In Diablo, this happens to Prince Albrecht when he is possessed by Diablo, and following the hero's sticking of Diablo's soulstone into his own head, he winds up possessed as well, and becomes the new Diablo in Diablo II.
In Doom 3 (and, quite possibly, the old Doom games) demonic possession turns people into zombies.
This happens to anyone possessed by a demon in Dragon Age.
Legacy of Kain: Raziel learns to occupy corpses and shape them into an image of himself.
When an Ing from Metroid Prime 2 fuses itself to a host, the host takes on a darker, mutated appearance as a direct result.
Super Robot Wars UX: Noval Dilan becomes the physical embodiment of Kali Yuga (with Durga's appearance) and grows to the size of a planet.
In Shin Megami Tensei IV, reading certain kinds of books will transform the reader into demons; this trope is implied in the process. It's most clearly seen in the case of Ogun and Dantalion, though Issachar and the victims of Red ingestion might also count.
Noted in the Whateley Universe as one possible consequence of a low-powered Avatar-type mutant hosting a too-powerful spirit as the spirit will make changes to the Avatar's body to make itself more comfortable. And the Avatar trait is already all about being superhumanly good at this sort of thing...
After being possessed by Zordrak in an episode of The Dreamstone, Amberley gains a pair of extremely evil looking glowing eyes.
Jackie Chan Adventures: the ghost of Shendu (a dragon-demon-wizard) usually gives his host glowing red eyes when in control. While he's not capable of transforming his host's body under his own power, he once tried to do so manually with potions.
In Adventure Time, the Ice Crown causes a physical transformation in its wearer, whom it tries to impose its own will on. As the person falls further and further under the Crown's control, they begin to develop blue skin, long white hair, and fangs (although some of these traits can vary depending on circumstance).
Happened a few times in The Real Ghostbusters, most notably in the episode 'If I Were A Witch Man', where we see the ghostly-witch Kestral possess two people - one of which being Egon Spengler - and she turns their bodies into the old stereotypical witch look (or in Egon's case, an old man).