"I live in the games. I search through systems, people, and cities, for this place: Mainframe; my home. My format? I have no format. I am a renegade, lost on the Net."
In more ways than one too. While Matrix and Andraia are lost on the Net, Bob is lost in the Web. At the same time Dot and Mouse are forced to abandon the Principal Office offscreen and are forced into hiding. The Tor also gets destroyed forcing Megabyte to find a new place to "set up shop". Seems like everyone in this show loses their home at one point or another.
Part of the series premise for Transformers: Beast Wars. Everyone was stranded on a strange planet far from their homeworld of Cybertron; at the end of the first season, this was revealed to be prehistoric Earth Earth All Along, far from their home time, which would be about three hundred years past our present day.
Subverted when Zuko betrays Iroh and is allowed to come back. Then subverted right back to straight when Zuko realizes it wasn't worth it and makes a Heel–Face Turn. And subverted again in the finale when he not only goes home, but he owns the home.
Also happened in The Legend of Korra to Asami Sato. After discovering that her father is an Equalist, she had to abandon her home and her previous lifestyle that came with it.
One episode did focus on the duo finding a way back home, but they opt to stay in order to protect the Princess.
In another episode, they did go back home, only to find out Koopa was terrorizing Brooklyn. They then tricked him into following them back to Mushroom Kingdom and blew up the way so he'd not be able to return to Brooklyn.
A conversation between the Martian Manhunter and Hawkgirl in an episode of Justice League notes that this trope applies to so many of them — Superman and J'onn are each the Last of His Kind, Hawkgirl is stranded light-years from home, and Wonder Woman has just been exiled from Paradise Island Themyscira — that they should call themselves the "Just Us League". It's even more poignant for the audience, who (unlike J'onn and Hawkgirl) know that Batman lost his family as a child.
This trope is played with in Hawkgirl's case. She is actually an agent sent by the Thanagarians to spy on Earth and its secrets. The Thanagarians eventually come to Earth and take it over. She then finds out that they are going to use Earth as part of a weapon against this one alien species they are at war with. Unfortunately, Earth would be destroyed once the weapon is activated. In the end, she ends up alienating a lot of people, causes a chain of events that lead to the destruction of Thanagar, and it takes a long time before she is allowed back into the Justice League. Wonder Woman eventually manages to work things out with her mother, and she is allowed to set foot on Themyscira again.
Danielle in Danny Phantom can't return to Vlad's manor where she was cloned and raised on the virtue that the owner is willing to kill her in order to make a better clone! She spends her time constantly on the move.
Gargoyles sometimes plays with this trope, for example in "Enter Macbeth," in which Xanatos is released from jail and free to return to his castle... forcing the titular gargoyles to leave said castle and find a new home. It doesn't stop them from visiting occasionally, though...
Also notable is the Avalon arc, where several characters spend much of the second season being dragged around the planet by a magic boat.
In the "Hunter's Moon" arc (the last canonical arc of the show), the clock tower where they've been living is also destroyed. Luckily, Xanatos owes them for saving his son and allows them to return the castle.
The Simpsons parodied this a Tree House of Horror episode where Homer inadvertently travels back in time and repeatedly makes changes to the world. After some time, he settles on a world almost identical but where everyone has long forked tongues.
"Eh... close enough."
In the last two episodes of Where on Earth Is Carmen Sandiego??, appropriately named "Can You Ever Go Home Again?" (pt. I & II), Carmen meets her father, Malcolm Avalon, who has believed for almost thirty years that she died in a fire. At first, he disowns her but later acknowledges her "willful determination" and seems ready to accept her. Then Lee Jordan captures him, and while Carmen and ACME are trying to rescue him, he falls off a roof and suffers amnesia, causing him to forget ever meeting her. Carmen resolves herself never to get close to him again.
"My God, it's the future. My parents. My co-workers. My girlfriend. I'll never see any of them again... [beat] Yahoo!"
Played with in Transformers Prime, Cybertron itself had been reduced to a lifeless planet with so little energon resources it can't contain more than a few small pockets of life. It isn't that they can't return home so much as there isn't much to return to. The video game Transformers: War for Cybertron suggests that the planet core was "rebooting" itself and would take eons to do so before energon production would continue, while late in the second season of Prime there is an option presented that might speed the process up. Too bad that option had to be violently removed from the picture...
As of the Beast Hunters finale, Cybertron is finally restored and the Autobots, and what remains of the Decepticons, return home.
Dreamy Smurf in The Smurfs episode "The Smurf Who Would Be King" thought this to be the case when he and his ship were dragged down a whirlpool and shipwrecked in the land of the Pookies...only for the whole thing to be All Just a Dream...Or Was It a Dream?, as finds a crystal similar to the ones that were in the land of the Pookies.
The whole premise behind The Many Adventures of Winnie the Pooh episode Home Is Where The Home Is. Christopher Robin accidentally breaks a statue of a family member and decides that he can't stay there anymore.
Oh No! It's an Alien Invasion: After the Brainlings kidnapped all the grown-ups they were supposed to leave Earth, but their leader Emperor Brainlius insisted on staying because he finds it a great party spot, much to the annoyance of his assistant Briiian who wants to leave.
Star Wars: The Clone Wars concludes with Ahsoka Tano on trial for multiple sabotages and war crimes. She's eventually cleared of all charges, but leaves the Jedi Order without hesitation because of the revelation that the Jedi Council, even when acting with honor and wisdom, is capable of cruelty and inhumanity that overshadows the Sith. This turns out to be a good thing, as almost everyone who stays affiliated with the Jedi Council is wiped out in Star Wars Episode III anyway.
Which allows her to survive long enough to become the grandmaster of the rebels. Then she finds out what happened to Anakin...
Steven Universe: The Crystal Gems can't go back to the Gem homeworld; their sinister plans for Earth led to Rose Quartz and the others deciding to stay and protect it. Garnet goes so far as to smash Earth's connection to the Galaxy Warp after Peridot repairs it, with the implication that they were the ones that broke it the first time.
Peridot winds up in the same boat as them and becomes a Crystal Gem after the events of "Message Received". This is mostly because Yellow Diamond, her boss and idol, tells her she's expendable, not caring in the slightest if she gets killed in the Earth-Shattering Kaboom that would happen when the Cluster hatches. The last straw, however, comes when Peridot tries to convince her that Earth is worth saving, if only for its resources, but Yellow Diamond goes into full-on Evil Is Petty mode and decides to destroy Eartth simply because the Crystal Gems DARED to defy her.