Whether it's real life or anime, not all romantic feelings can be reciprocated. Sometimes no matter how much one person loves another, those feelings just don't reach the other person.
Anime characters whose love went unrequited can appear in any genre. Though common in the romance and slice of life genre, they also appear in more action-oriented series like Parasyte and Naruto. In some cases, these hopeless lovebirds never get over their feelings and never find anyone who does return their feelings - but in other cases, they do move on to better things, be that an actual relationship or personal growth outside the arena of romance.
While one-sided love can add tension to a storyline or deepen a character, it can still be pretty sad. Let's take a moment to appreciate the characters who just couldn't get the other person to love them in the same way.
Rem is a maid who suffers from a major inferiority complex. After Subaru rescues her from danger, she falls in love with him. Despite her shyness, she's blatant about her feelings, often asking him for praise or signs of affection. When she ultimately confesses, she's turned down, because Subaru is in love with someone else. Emilia offers to be his second wife, which Subaru accepts.
This isn't really what Rem wants, but she's accepting whatever scraps of love come her way. Even worse, she winds up comatose before she can receive the paltry affection he does offer.
Sayaka Miki's unrequited love story is one of the sadder ones on this list. She was so smitten with her classmate Kyousuke Kamijou that she became a magical girl so that she could wish for his recovery after an accident left him unable to play the violin. Sayaka assumed that if she did this for him, he would be overcome with gratitude and that he would fall in love with her. Not only did Kyousuke not even realize that Sayaka was behind his miraculous recovery, he starts a new relationship with someone completely different without ever knowing how Sayaka felt. This is one of several factors that leads to Sayaka becoming a witch and having to be destroyed by her friends.
Tsubaki Sawabe is Kousei Arima's childhood friend. It takes her a long time to fully understand her own feelings - at first, she sees them as very good friends and nothing more. Though she does ultimately accept the nature of her feelings for him, she can't work up the nerve to confess. Kousei ultimately ends up falling in love with Kaori Miyazono, and although she loves him back they never pursue a relationship, because Kaori dies of an unnamed illness before such a thing is possible. Tsubaki accepts that her relationship with Kousei will never move beyond friendship, and decides to continue supporting him as he pursues his musical career.
Though Misa Amane does manage to finagle a relationship with the love of her life, Light Yagami, it's quite clear that he doesn't feel anything resembling love for her. Light sees Misa as a combination of annoying and convenient. He doesn't exactly relish her gushy affection, but her willingness to do literally anything for him causes him to see her as a tool to help him fulfill his murderous ambitions. This isn't exactly what Misa wants from Light, but when you're a desperate stalker who is trying to use your pseudo-relationship to cope with your parents' brutal murder, you'll take anything.