A character who has just gone through some sort of trauma, learned something they probably didn't need to know, or seen something they really shouldn't have had to, will often have an unfocused, vacant stare into a vast abyss of nothingness, slipping into a shock and weariness from which it is very hard to shake.
Note that this trope describes the stare/facial expression itself, and not what causes it or anything related.
The term "thousand-yard-stare" is believed to have originated in World War One, and was coined for the faces of battle-weary soldiers. Named for the perception that such stares really do seem to be able to see very far ahead. Eyes cross a little when focusing on something reasonably close, but eyes not looking at anything will behave like eyes looking at something very far away. Dull Eyes of Unhappiness can look similar to this, but they're chronic while this trope tends to be transitory.
See also Heroic BSOD, for what usually goes hand-in-hand with this. Not related to the 'Thousand Yard Stare of Impending Flashbacks', an affliction near universally shared by the characters of Lost.
In Fullmetal Alchemist, Mustang and Hughes discuss it during the Ishvalan war. Hawkeye approaches, and Mustang laments that Hawkeye has the stare too.
In Full Metal Panic! The Second Raid this happens when Sousuke believes he's failed in protecting Kaname. This happens again after Gauron tells Sousuke that Kaname was killed by Yu-Lan and Sousuke snaps.
In the Marineford arc of One Piece after Ace gets killed.... oh God, the look on Luffy's face, of all people.
Zoro's expression after taking all of Luffy's pain in Thriller Park. It even got to the point of almost being a case of Died Standing Up until Zoro speaks up and says "Nothing happened."
Vash the Stampede is prone to this expression when pushed far enough. Even leaving aside his Heroic BSOD after Legato's death, he will do this while smiling sometimes.
Nothing emphasizes his isolation from humanity better or more tragically than a sad-Vash thousand-yard-smile, especially if he's doing something like hugging Miss Elizabeth while she breaks down over his not being evil, after trying to blow up the town to kill him.
Rurouni Kenshin starts doing this when his angst level picks up late in the manga, though his first uses are after taking absurdly heavy damage in the Shishio arc. Maxes out during his especially persistent Heroic BSOD and 10-Minute Retirement to the slum of despair. Scares everyone in its first major appearance right after Enishi formally declares his Jinchuu.
A less pitiful-looking version was also employed back when he was Hitokiri Battousai, aka Teenage Kenshin, and attempting to put off his moral crisis and shellshock for as long as possible so as to fulfill his duty.
Chibodee Crockett of G Gundam has one while wandering around in a (somewhat violent) daze resulting from his clown phobia.
Kira Yamato of Gundam SEED and Gundam SEED Destiny looks like this following the conclusion of the Bloody Valentine War. He spends most of his time sitting on his porch, staring off into space, and flashing back.
This serves as another deconstruction for Casca's post-Eclipse behavior in Berserk. After going through a very heinous ordeal of being raped by her former captain-turned-demon lord Griffith right in front of her lover Guts, Casca shows very realistic signs of rape trauma syndrome, one of them being that she often vacantly zones off and stares at nothing. Prominently shown on the hilltop scene when she miscarries her baby.
Guts showed very similar signs the morning after his own traumatic rape at Donovan's hands back when he was a little boy.
In A Cruel God Reigns Jeremy displays this very often, every morning after his stepfather sexually or physically abuses him. As the series progresses, his gaze becomes like this most of the time, especially when he is close to one of his several instances of Heroic BSOD.
Payback: The thousand-yard stare. A marine gets it after he's been in the shit for too long. It's like... it's like you've really seen beyond. I got it. All field marines got it.
Joker himself gets to do the stare after shooting a sniper as a Mercy Kill.
One of the soldiers on leave in Band Of Brothers (the whole episode focused on various soldiers dealing with the sudden change from battle to civilian life) has this.
Commonly, the expression on some of the characters in Saving Private Ryan (indeed, the beginning graveyard scene ends with this).
Enforced Method Acting: The entire cast was run rugged, interminable military exercises - except Matt Damon (who plays Pvt. Ryan). It even made the cast resent Damon, which was entirely the point.
WWII veteran and b-movie star Audie Murphy, who saw many of his comrades in arms killed and is credited with personally killing, wounding or capturing more than two hundred Axis soldiers, had a particularly bleak and distant stare, which director John Huston put to good use in The Red Badge Of Courage. Murphy developed a warmer and somewhat more animated screen persona around 1953, perhaps due to the birth of his beloved son Terry, but he never really lost the Thousand Yard Stare.
If there is a fetish for thousand-yard stares, the film version of The Road is your fuel.
Boogie Nights: During the scene at Rahad Jackson's house, a drug-addled Dirk stares into space for what seems like an eternity.
Invoked in Rambo, the fourth film in the series, when an Australian mercenary informs Rambo that he's seen the thousand-yard stare before. He's not impressed, but his opinion changes after the shit hits the fan.
In Animal Kingdom, Darren, the youngest Cody brother, develops one after getting raped in jail.
In District 9, Wikus has one of these in the back of a MNU van after he has crashed Christopher's command module and has been apprehended by Koobus.
In the film of "Battle Royale", Yuko has one just before she tries to poison Shuya and ends up killing all of her friends.
In Rango, one of the supporting characters goes into this as a "defense mechanism" to keep her from recognizing her abandonment issues with her dead father.
Marius from Les Miserables sports one of these after the events in the barricades. It takes a love song from Cosette to pull him out of it.
Angela in the original Sleepaway Camp has one of these. It's one of the most memorable aspects of the film.
Some (canonical) DVD specials from Doctor Who have noted this about Rory Williams. He spent almost two thousand years guarding a box as an immortal centurion. It happened in a defunct timeline, but he still has the memories, which he must suppress for his own sanity, though as the Doctor points out "Sometimes you catch him just staring..."
He mentions that he can remember all two thousand years he stood guard, he just doesn't try to remember it.
The Doctor himself does it sometimes, but usually only when he's alone or his companions aren't looking. Eleven in particular.
Amy does this after the Doctor is apparently killed.
Archie would stare blankly when troubled in Series One quite a lot. Being ruthlessly tormented by a shipmate followed by being presumed dead, imprisoned by the enemy, and punished painfully for escape attempts and then getting caught up in someone else's war where the chances of survival/victory are extremely low will have an impact on a person.
Horatio Hornblower gets this unfocused look when he's troubled by something or somebody and when he goes into his "questioning my abilities" mode.
Mal Reynolds has an empty shocked stare in the Firefly pilot at the end of the Battle of Serenity Valley. He gets it from not getting any backup, from losing everyone under his command except Zoe, from losing the war to the evil Alliance.
Referred to in the song "Assassing" (sic) by Marillion.
Shown in the music video for "Ghost of You" by My Chemical Romance, much of which is set during the landings at Normandy during World War II. The music video ends with a shot of the lead singer's stunned eyes.
Referred to more humorously in Tom Smith's "Rich Fantasy Lives"
"That waitress at Pete's who took so long to seat you and left you to stand in the doorway. With her stringy red hair and her thousand yard stare, in her mind, she's the princess of Norway."
Referred to in Pink Floyd's "Shine On You Crazy Diamond" - Now there's a look in your eyes / like black holes in the sky - describing the look Syd Barrett sometimes wore on his face during his Creator Breakdown.
Wrestlers who take powerful blows to the head are often described as having this, and it is usually an accurate description. Randy Orton, during his brief face run a few years ago, was involved in a story line where he was taking too many bumps to the head, and had this blank stare after each one.
In particular, Chris Benoit was described as having this for much of the last year of his life, outside of the ring.
Played for laughs in one of Bill Bailey's routines, wherein he describes a conversation with someone about swimming with dolphins; apparently, the dolphins the other person had swam with were ex-military dolphins which had been used for underwater bomb training, and had "a glazed, faraway look in their eyes."
Bill Bailey:[As the dolphin] You weren't there, man; you weren't there.
Walker in Spec Ops The Line has two, one each at a significant moment in the plot. The first is when he finds the corpses of civilians among those of the enemy soldiers he ordered to be bombarded with white phosphorous mortar. Walker delivers his lines with steely calm, but the moment at which he snaps is still chillingly clear. The second is the climax, when he realizes the man he hunted down and committed atrocity after atrocity to find is already dead; Walker has been imagining a taunting voice to create an enemy to blame for his own crimes.
Lara Croft ends up sporting one of these after her hellish experience on the island in the 2013 reboot of Tomb Raider.
Ariel from Drowtaleshas this expression after she's forced to choose between killing an enemy who tried to kill her and fighting her cousin to the death. She chooses to kill the enemy, and it's strongly implied this leaves her with PTSD. Even worse, she's physically the equivalent of a seven year old child when this happens and the victim is the same age.
In an episode of SpongeBob SquarePants the eponymous sponge blanks out after receiving an improbable order. Mr. Krabs explains it as the thousand yard stare to Squidward, that he had seen it during the war.
Donald Duck's stuck with one at the end of "Up A Tree", after Chip n' Dale blew up his house into smithereens.
Used in Adventure Time frequently. Finn gets one in Susan Strong when he contemplates being the last of his kind for too long. He gets another one in "Marceline's Closet," when he sees Marceline naked.