There's a strong argument to be made that the entire sub-genre of Pop Punk is built on this trope.
The They Might Be Giants song "Withered Hope" is about about a Love Pentagon that's like this. A Very Sad Sack loves Withered Hope, who has a soul mate, who loves a picture of a crook, who loves a motorcycle, who loves Very Sad Sack
You love her, but she loves him And he loves somebody else, you just can't win
Quite the theme for The Smiths. "I Know It's Over", "I Want The One I Can't Have," "There Is A Light That Never Goes Out", "Back to the Old House", etc.
The Aqualung song "Strange and Beautiful" is the very definition of this trope. The song is about how the protagonist wants someone and wishes they could put a spell on them to make their love requited.
Vanessa Carlton's song "Rinse" is about all unrequited love, and it states that the girl in the song should give up her love for a guy who doesn't love her back but can't.
"Two Out of Three Ain't Bad" by Meat Loaf: The singer can't love the girl he's singing to, because he's in love with another woman who, true to the trope, doesn't love him.
"Everybody Plays the Fool", a song with famous versions by R&B group The Main Ingredient and by Aaron Neville.
The Burning Hell's song "Grave Situation, Part 3" describes a love quadrangle involving "a man who loved a man who loved a woman who loved another man"
In "Living Next Door to Alice", most successfully covered by Smokie, the narrator has been in love with his neighbor for 24 years, but couldn't tell her. And now she's moving away. Meanwhile, the narrator's friend, Sally has been in love with him for 24 years, but he ignored her because of Alice.
Kotaro has a crush Hina, but she likes Koyuki, who is in love with Natsuki.
Souta fell in Love at First Sight with Akari, who's not really interested in romance yet (although the official website mention that she might have a liking for Haruki).
Weirdly, Haruki and Mio have unrequited love for each other. They're both interested, but neither found the courage to confess until they both graduated and moved on from each other.
Vertical Horizon's "Everything You Want" is about pining for someone who doesn't love you back.
Unrequited love, and relationships with people who are taken occur frequently as themes in Hobo Johnson's songs. "Peach Scone" and "Mover Awayer" are pretty much all about loving someone who's not interested.