The Isekai genre of anime has become more popular of late, and each season brings with it new contributions toward the growing collection of protagonists that find themselves in an alternate world.
While many of the protagonists are the Everyman character and something of a standard blank slate, there are some who have most definitely left a terrible world and life behind in order to find themselves in their new home.
Whether this world is a dystopian future or a reflection of the hardships of the real world, these characters have the opportunity to find their own happiness in this other world.
5 Overlord
Suzuki Satoru's home world is barely mentioned in the anime of Overlord; however, there is a lot of information available from the light and web novels. In an alternate future of 2138, the Earth has become polluted beyond recognition, with the sun barely making an appearance behind smog so thick that anyone going outside needs to wear a mask. Without the sun, plants died and without plants went insects, then birds and mammals, and torrential acid rain fell regularly.
Government was practically non-existent, and everyone lucky enough not to be living on the streets in this polluted world worked until they couldn't take any more and died. Suzuki Satoru lived in this world where every day was a nightmare hellscape filled with work until he could escape into his virtual world. Considering the world he came from, it's perhaps understandable why Momonga is so uncaring of human life in the new world.
4 Harem In The Labyrinth Of Another World
Michio Kaga is intended to be something of a normal high schooler, and little is made of his background in the anime, suggesting that he simply wanted to play a virtual reality game. The original source material, however, explains a little more about Michio's background and why he was looking for this escape. Michio's early life was filled with perpetual bullying from the other children in school. In an attempt to prevent this, he began learning how to fight, though even with this effort, very little changed as he grew up.
Moving into his teens, he was treated like an outcast, and he grew to hate the world that he lived in. So severe were his feelings that he accidentally found the path to another world on a suicide website, the advertisement suggesting that rather than suicide, he could instead leave that world behind. While he may not have taken it seriously at the time, the decision put him in a position to find happiness of his own.
3 By The Grace Of Gods
Ryoma Takebayashi was a 39-year-old man whose life revolved around his work. He was constantly being relied upon by others, and he accepted it all without a word and took on more and more work from others while his boss frequently abused him and threw beer bottles at his head. This all happened after a childhood filled with abuse from his father, a man who was frequently violent and assaulted him.
After the death of his mother, Ryoma grew emotionally distant and simply accepted the world around him, accepting work as a (literal) workhorse and hunting pigeons to survive. Outside his work, he barely had time for anything else and spent his time reading or meditating. He had no friends and had never been in a relationship. Finally, Ryoma passes away during his sleep due to a brain hemorrhage and is reincarnated by gods who took pity on him following these years of torture.
2 Re: Zero - Starting Life In Another World
While some isekai protagonists can come from difficult backgrounds, Subaru Natsuki is in some ways at fault for his own unhappy world before his otherworld abduction. With his parents being strange but caring and his father being somewhat of a celebrity in the community, Subaru idolized his father and wanted to live up to the man he knew.
While this was simple enough as a young child, he found this more and more difficult to achieve as he grew older and encountered other skilled and talented people. Subaru's own shame at being unable to live up to his own expectations of himself resulted in him desperately trying to stand out by doing more outrageous things. Eventually, he drove all his friends away with his behavior, and he grew to loathe himself, the feelings of which he carried with him to his new life.
1 Mushoku Tensei: Jobless Reincarnation
While the person Rudeus was is never named, the man he used to be was a 34-year-old NEET who lived a shut-in life. His condition grew from relentless bullying in school and his obsession with computers letting his grades drop. He was an outcast and someone who was mocked by the rest of the school, with one notable example being when someone cut in front of him, and he tried to tell that person off.
Unfortunately, this pupil was his upperclassman who beat him up, stripped him naked, hung him up, and took pictures of his naked body to distribute around the school. After chasing away any and all friends, Rudeus shut himself away and couldn't stand leaving his room, not even for his parents' funeral. This resulted in his encounter with the teenagers and a truck that killed his adult body and transported his soul to another world.