Pretty much everyone in 7 Seeds. Some even try to get back home, but they don't like what they find.
Berserk: Guts had to flee from his original mercenary band after he killed his adoptive father in self defense and the other members sought to avenge their leader's death. Later, it was revealed that Casca joined the Band of the Hawk because if she were to go home, she would be arrested and tortured for killing a noble in self defense of Attempted Rape. On the grander scale of things, the whole Band of the Hawk was forced to flee the Kingdom of Midland upon Griffith's arrest for high treason - which was popping the cherry of the princess.
Faye Valentine from Cowboy Bebop. She eventually finds the spot where her home used to be, only to discover there's nothing there now, not even ruins. She draws the layout of her house, as well as a rectangle where her bed used to be, in the dirt, and lies there alone.
In fact, if you're willing to extend this to psychologically or spiritually being unable to return to home, then the entire main cast could count. An underlying theme of the series seems to be that the Bebop is the only home Spike, Jet and Faye have left, hence why they default to return to it whenever they strike out on their own.
In Fullmetal Alchemist, Ed and Al burn down their house so they won't be able to give up their mission. Of course, Pinako and Winry's house is always open to them, so they're not as homeless as they'd like to think.
Hohenheim is convinced they did it so as not to face up to the whole "brought back an abomination of nature instead of our dead mother" thing every time they walked by the study.
"It's no different from when a child wets the bed and then hides the sheets. You were running away...Edward."
In NarutoItachi Uchiha. After killing his entire clan on orders he can never return to Konoha without dying or starting a civil war.
To a lesser extent, Sasuke Uchiha. After learning the truth of Itachi's actions, he no longer has any concept of home; all he wants is to make everyone else suffer.
Obito Uchiha, later known as Tobi. He's rescued from certain death by Madara, but the cave that they are in has the exits blocked off (intentionally) with a giant boulder, so Obito literally can't leave. Eventually something happens that causes Obito to completely lose any desire to return, however.
Jimbei tries to avert this when he becomes a Warlord of the Sea. One of his requirements for joining is that the World Government would allow any ex-slaves to return to Fishman Island. However, once Jimbei resigned from his position, the pardon was revoked and the remaining Sun Pirates were forced to leave.
In Princess Mononoke, Ashitaka is permanently exiled from his home village to protect everyone from his curse.
Ranma ½ - Ranma can't go home because his father made a vow to his mother that if he failed to make their son into a real man, father and son would commit seppuku and their mother would be the one to cut off their heads — and turning into a girl when splashed with cold water is pretty much the opposite of being a real man. Ryoga can't go home because he can't find it, and it's not like his parents would be home if he did. Shampoo can't go home until she claims Ranma as her husband. It's not clear if Ukyo even had a home other than her dad's okonomiyaki cart.
In Record of Lodoss War, Parn is kicked out of his village at the beginning of the story. He dons his father's armor and subsequently burns his house down and from then has to go Walking the Earth.
Rurouni Kenshin: To save his father and his siblings from retaliation after he delivered a beating to criminals ruling the region where they lived, Sanosuke left them forever.
Kenshin himself can't go home because he was an orphan, and bandits murdered the girls who were attempting to take care of him. Kenshin's internalizing of this trope is a major motivator in the second and third arcs of the series.
Holo of Spice and Wolf. Her hometown might be the only place she belongs, and it's rumored to have been destroyed centuries after she left. Even if it still exists, she knows that the passage of time has likely changed it into something completely different. She won't give up until she acknowledges it herself, though.
Spirited Away has young Chihiro and her ignorant parents wander into what appears to be a bankrupt theme park and explore. Long story short, she is forced to sign a contract, which turns her into Sen, a serving girl who must work in Yubaba's Bath House of the Gods for all eternity, unless she wants her Transformation Trauma'd parents to be ground up and made into sausages. The whole point of the film is her learning how to be more mature and resourceful in order to reverse this fate.
Tsubasa Reservoir Chronicle: Syaoran can't go home because he wasn't meant to exist in the first place, and he and his replacement Watanuki are stuck in similar predicaments: Syaoran will wander the worlds forever while Watanuki is stuck in the The Little Shop That Wasn't There Yesterday forever, least their existences destabilize time and space. At least they both have company, which includes Faye, who destroyed his world.
Youko spends the first arc of The Twelve Kingdoms trying to get back to her own world. Eventually, she comes to realize that she is needed far more in Kei than she is at home, and reluctantly agrees to become the Glory-King.
Honestly, every kaikyaku ("People from Beyond the Sea") deals with this, since going to the "12K" world is a one-way tripnote The only kaikyaku who aren't absolutely miserable in the new world are those who were meant to be there in the first place (like Youko, Enki, and King En), or those who are given the gods' blessing and become immortals (Suzu, although it takes over a century for her to cheer up). This is due mostly to the Kingdoms' language being utterly incomprehensible to outsiders, and also prejudice. In the animated version, Yoko's companions Sugimoto and Asano (the latter an anime-only character) both have to come to grips with this.
This happens in Vampire Princess Yui, after Yui's powers fully awaken and her last surviving relative, her grandmother, died.
In the later installments of Super Dimension Fortress Macross franchise, there are colony ships and it is implied that it is virtually impossible to travel back to Earth from such a ship, at least unless you happen to be very rich and / or infuential.
Several characters deal with this in Attack on Titan, with many a Doomed Hometown due to invasions by Titans. Mikasa lost her childhood home when kidnappers murdered her parents, though she's immediately adopted into the Yeager family. A year later, Shiganshina is destroyed and the main trio of Eren, Mikasa, and Armin are left living as refugees. Hannes discusses this trope, longing to return to the peaceful days of the past....but he's killed while protecting Eren and Mikasa, who realize those days can never be reclaimed. Reiner and Bertolt, fellow refugees from Wall Maria, are driven by their desire to return to their lost village.....though Reiner acknowledges this trope, admitting there's nothing left to go back to. Though they do head back to their true home after their cover is blown, it's fairly clear from their Becoming the Mask that Reiner was correct about the "home" of their childhood being gone. After three years away, Sasha finally returns home to find her village unrecognizable — what was once an isolated hunting village deep in the forest is now a clear-out farming village that raises horses. And in a particularly heartbreaking example, Connie's village is destroyed when the Beast Titan transforms the villagers into Titans. Barely holding back tears, he states that he no longer has a home to return to.
All three main characters in Tokyo Godfathers- Gin, Hana, and Miyuki- believe this. Gin because he left due to being unable to support his family, believing they'd be better off without him; Hana because she lost her temper and attacked a heckler during her singing act at her mother's bar; and Miyuki because she believes her father will have her arrested for stabbing him in the heat of the moment during a fight. Ultimately, over the course of the story, all three are proven wrong in the best way possible.