An Odd Place to Sleep

Showing a character's sleeping habits can tell the audience a lot about their character. Often an indication that a character is a bit off is if they have Bad Dreams, or in some cases, don't sleep at all.

And then there are characters who sleep in strange places. Showing a character who habitually sleeps in a place other than a bed may serve to indicate that the character in question has a few odd personality traits, or that they're not altogether there mentally, or that they're just not used to sleeping in a bed for whatever reason. It can also be used to show that a character is not human, and therefore it might be perfectly normal for members of their species not to sleep in a bed. The main point is that the trope is used to set the character apart in some way, or to indicate something specific about their character.

A very common version of this is characters who are used to discomfort or hardship - homeless people finding a shelter somewhere in a city, outdoorsmen camping in the wild, front-line soldiers in forward camps or berths not entirely designed for humans - who are offered a bed in the lap of luxury, but find it impossible to sleep in.

If a character doesn't sleep in a bed because there isn't one available, it's not this trope. There Is Only One Bed is when a character gives up the bed out of necessity or a sense of honor.

Examples of An Odd Place to Sleep include:

Anime and Manga

In Appleseed, Deunan sleeps on the floor instead of the bed after being taken from the wasteland into Olympus, probably because she's used to a hard surface.
Similarly, Sousuke Sagara of Full Metal Panic! makes a habit of sleeping under his bed, as a manifestation of the paranoia he carries over from his years as a Child Soldier. And, considering the extremely limited space and the decided uncomfortableness of the area in question, sleeping there tends to noticeably deter any of his many admirers from trying to cop a feel on him while he's asleep.
In Strike Witches, Francesca Luccini often sleeps in high, perched, narrow structures like tree branches and beam girders, possibly reflecting her Catgirl nature.
Roronoa Zoro of One Piece tends to sleep on the deck of the Straw Hat's pirate ship whenever possible... even in the middle of devastating storms. He's also been known to take naps in snow drifts while half-naked.
THE iDOLM@STER - Miki can sleep most anywhere, this includes the trunk of a van, two or three foldable chairs, and even while Haruka is piggybacking her in the Live For You OVA.
Claymores only bother to sleep every few days, but Theresa of the Faint Smile was seen as unable to even rest in the best room of a local inn until she planted her BFS into the floor and sat to lean against it.
Coyote Starrk of Bleach sleeps on a green beanbag chair. If an omake is to believe, Lilynette can sleep on top of Starrk.
In Tenchi Muyo!, Ryoko tends to sleep in the rafters of the Masaki home.
Shimakaze from the Kantai Collection anime.

Comic Books

In Bar Sinister, Sigil sleeps hanging upside-down because she is part vampire bat.

Film

In the 2002 movie adaptation of The Count of Monte Cristo, Edmond Dantes is shown to sleep on the floor instead of in a bed after being imprisoned for so long.
In the 1980s Batman movie, Bruce Wayne is briefly shown sleeping hanging upside down from his rack. This is never mentioned again.
In the Daredevil film, the title hero is shown to sleep in some kind of sensory deprivation tank because of his heightened senses.
Cast Away. Tom Hanks sleeps on the floor for a while instead of an available bed.
Munich. After planting a bomb in a terrorist's bed, one of the protagonists can only sleep in a cupboard.

Literature

In the Discworld novel Wyrd Sisters, one of the late King of Lancre's servants unexpectedly finds himself the new king. A later novel reveals that he sleeps on the floor just inside the door of his bedchamber instead of in his bed, because he's always slept on the floor, usually the floor just outside his master's door — and now that he's king, the kingdom is his master.

Live-Action TV

Jim Profit in the short-lived television series Profit regularly sleeps naked in a cardboard box, just like the one he was raised in by his abusive father.
Mork and Mindy: Mork sleeps upside down in the closet because he's an alien and that's how they feel comfortable.
The Addams Family: Fester, or perhaps even several of the Addams, like to sleep on a bed of nails.
In an episode of Dexter, Dexter breaks into Lumen's hotel room and sees that she has made up a bed in the closet, since a closet was the only place where she felt safe from the men who raped her.
The eccentric genius protagonist of Probe sleeps in a cupboard. When he was young he couldn't afford a proper sensory deprivation tank; by the time the series starts, he can afford as many as he likes, but he's gotten used to the cupboard.
Early on in The X-Files, Mulder sleeps on his couch (when he does sleep), in large part because he's using the bedroom for storage. This does change in later seasons.

New Media

Lady Slaughter in Descendant of a Demon Lord is irritated by the presence of living creatures (except Celes) and tries to sleep some distance away from them. Which is probably related to her sleeping in strange places. Celes has found Slaughter sleeping in a crevice and a crate.

Newspaper Comics

Snoopy in Peanuts is shown to sleep on the roof of his doghouse.

Video Games

Laharl from Disgaea sleeps in a coffin, despite not being a vampire.
Gravelord Nito from Dark Souls sleeps his days away in a coffin, overseeing death. Siegmeyer can fall asleep anywhere. This includes volcanic lava filled ruins, and while standing in a deathly poisonous swamp.

Western Animation

Futurama: Bender, and by extension, all robots, prefer to sleep standing up in a room small enough to be a closet.
Similar to the The Addams Family above, Misery in Ruby Gloom sleeps on a bed of spikes. Anybody else who sits on her bed will usually have a pillow to sit on, too.
A Running Gag in the Christmas Special Yogi's First Christmas is Yogi (who, seeing as it's winter, is supposed to be hibernating) being unable to stay awake and constantly falling asleep at the most inopportune places and times.

Real Life

Thomas Edison kept a mattress in the closet in his lab. He was almost totally deaf, so the noise from people working didn't bother him.
A Chinese ruler slept on a wooden bedframe and kept a piece of bitter gall hanging near it to lick, so as not to forget the hardships he went through as the prisoner of an enemy state.
There's a man (possibly featured on Ripley's Believe It or Not) who had a medical condition that required him to never lie down. Therefore he made a box he could sleep in while sitting. He did get over the condition, but by that time had found his box so comfortable that he kept using it.