The quote at the top of this page is provided by the amusing song "Jimmy Olsen's Blues" by the Spin Doctors from the early 1990's and featured the Daily Planet's favorite cub photographer lusting after Lois Lane and jealously grumbling about Superman. The song, despite being a catchy Ear Worm and a minor hit, actually didn't reflect the situation in the comics, where Jimmy didn't actually have any romantic interest in Lois and was famously known as "Superman's Pal, Jimmy Olsen." That being said, the song got Jimmy's name back into the pop culture mainstream, and for a while comic book artists actually drew Jimmy wearing a Spin Doctors t-shirt as a Shout-Out. Also, more than a decade and a half later in Superman: Birthright, the author added the detail of Jimmy having a bit of a crush on Lois.
This trope most often turns up in the case of love songs written for someone who is, well, already taken. Examples include:
The Seven Deadly Sins series by Vocaloid producer Akuno P aka Mothy. Envy's song is Tailor Shop on Enbizaka by Luka Megurine. She's shown to be a hard working tailor, constantly thinking about her "lovely person". This gets more twisted as the song goes on.
"Jessie's Girl" by Rick Springfield probably deserves mention here.
Cher Lloyd's "Want U Back" is about a girl who thought she was too good for her boyfriend and dumps him. Expecting him to be heartbroken, she's the one in the dumps when he bounces back and gets a new girlfriend. It is not a Green-Eyed Epiphany, she's jealous because the guy doesn't need her anymore.
Patty Loveless' "Jealous Bone" is about a woman who can't handle the thought of the one she loves with anyone else.
While the chorus of Lee Ann Womack's "I'll Think of a Reason Later" tries to paint what the narrator's feeling as Irrational Hatred, it's pretty obvious that the reason the narrator hates the new lady in the life of the man she loved is this trope through and through — she even mentions "having the slightest of a jealous bone" that tends to get larger when she sees him with her.
Beyoncé has a song called "Jealous" in her 2013 self-titled album.