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.
"Who" by Disturbed is a subverted example. The narrator was in a happy relationship at first, but his partner fell out of love with him for no apparent reason, leaving him wondering if things can ever go back to the way they were.
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.
I'm the guy she turns to When her lovers leave I'm the wildcard she's got up her sleeve But she don't look at me With eyes on fire Glowing like coals in the night Hungry eyes, burning with love and desire
"Brandy" by looking glass is the story of a port-town barmaid named Brandy who has to deal with her love, a sailor visiting the town, being more attached to the sea than to her
Yeah, Brandy used to watch his eyes When he told his sailor stories She could feel the ocean fall and rise She saw its ragin' glory But he had always told the truth, Lord, he was an honest man And Brandy does her best to understand She hears him say, "Brandy, you're a fine girl" "What a good wife you would be" "But my life, my lover, my lady is the sea"
"Creep" by Radiohead is about this. When the singer actually approaches the woman, she flees from him ("She's running out the door"). He tries to make peace with this: "Whatever makes you happy/Whatever you want..."
"When in Love with a Blind Man" (the B-Side of "Head over Heels") by Tears for Fears is about being in love with a man who's oblivious to your romantic feelings.
"Love's Unkind" by Donna Summer. The singer loves a guy who instead asks her best friend to the high school dance, and the spoken word bit adds "but she don't care, she loves someone else".
"Maureen" by Fountains of Wayne. At first, the narrator seems merely annoyed with his friend Maureen's constant, heavily detailed descriptions of her romantic exploits, but it's soon revealed that it bothers him even more because he has a crush on her and she doesn't seem to notice.
I know you think I'm just a friend But can we please just put an end To all the graphic imagery that you insist on feeding me You can't accept I'm not the one Who's getting to have all the fun And maybe that's what friends are for But I just can't take it anymore!
Stated explicitly in the opening verse of "Ones Who Love You" by Alvvays.
Take, take from the ones who love you, ooh Leave, leave with the ones who don't, ooh Lie, lie to the ones who like you, ooh Lay, lay with the ones who won't