Interestingly enough, the well-known song by The Bee Gees/Yvonne Elliman that shares this trope's title has this trope subverted. If she couldn't have him, she wouldn't stop him from pursuing others instead- but she'd keep herself from pursuing relationships with others instead.
For dreams that never will come true
Am I strong enough to see it through
Go crazy is what I will do
If I can't have you
I don't want nobody baby
If I can't have you, uh-huh!
Tony DiBart's 'The Real Thing' uses this trope as song lyrics in much the same way.
Dream Theater's concept album Metropolis Part II: Scenes from a Memory has this as an important part of the main plot. It's how Victoria died.
The Megadeth song "Loved to Deth": "If I can't have you, then no one will/And since I won't, I'll have to kill..."
Tom Jones' "Delilah", in which a man catches his girlfriend cheating, fatally stabs her, and pleads for her to forgive him. It's quite catchy.
The mothy song The Tailor of Enbizaka sung by the Vocaloid Megurine Luka has her pulling one of these when her lover is seen with at least three other women. The twist is that her "lover" doesn't even know her, and the other women were his family.
Another Luka song, "Love Disease" by madaco, heavily implies that she murders her love interest at the very end, after having murdered the hypotenuse only to have said interest try to get away from her.
I've watched you whore yourself for one more thing Why don't you sell yourself for one more? There's always one more thing Why don't you sell yourself If I can't have you, NO ONE WILL!!!
"Goodnight Socialite" by The Brobecks includes this trope in the chorus.
"Pick up the Phone" by Falling in Reverse, which is about an abusive relationship from the perspective of the jealous boyfriend, features the line "I'll be damned if I see you with some other man; If I cannot have you then nobody can"
The Barenaked Ladies song "Straw Hat and Old Dirty Hank" is an intensely upbeat song about the devotion a farmer has to a lady who is special to him. He's actually a stalker, the lady is a singer, and he shows up at her house bearing "flowers and a twenty-two with shells."
"The Last Mistake" by Assemblage 23. "If I can't have you, nobody can".
"Henry Lee" by Nick Cave and PJ Harvey: "Lie there, lie there, little Henry Lee, 'til the flesh drops from your bones. For the girl you have in that merry green land can wait forever for you to come home."