The narrator of "The Rake's Song" by The Decemberists murders his three children in an attempt to regain his freedom. He gets away with it, and isn't even bothered with feelings of remorse or guilt over it.
The Evillious Chronicles, being a series centered around exploring themes of good and evil, is prone to having a few of these. Most notably...
The titular character of Evil Food Eater Conchita. Though she does end up dying, namely by devouring her own body, the fact is she never really suffers any true consequences for committing horrific acts of cannibalism and Necromancy—even in death, she got what she wanted (to eat every food imaginable) and proceeded to Ascend to a Higher Plane of Existence by becoming a demon. At the end of the series, she effectively gives karma the middle finger by accepting an offer to use otherworldly technology to fly to alternate worlds with her servants so she can sample their denizens in search of the ultimate evil food.
Seth Twiright, the series original Big Bad, goes without any real punishment throughout the series. At the end, it's even implied that he got to reincarnate with everyone else in a new world (though in his defense, he did help save the world from the final Big Bad)!
Flower of the Plateau, in which Mikulia Calgaround kills two people, an ex-suitor/client and her own son because they're the only ones who know that she used to be a prostitute. Yet still nobody found out about that.
Bob Dylan's song "The Lonesome Death of Hattie Carroll" tells the story of a wealthy white man who kills a poor black woman in 1960s Baltimore, and receives a six-month sentence in punishment. It's based on a true story.
Billy Preston's 1972 song "Will It Go Round In Circles":
I got a story, it ain't got no morals Let the bad guy win every once in awhile I got a story, it ain't got no morals Let the bad guy win every once in awhile....
I had my fun, I'm going back to the place I don't call home There's no one there who waits for me, but you won't hear me moan My ex-wives all sue me, and with half my kids in jail I'll still come out laughing, coz me? I never fail, loser!
"Lay Me Down" by Dirty Heads is about a couple that robs a bank, shoots a sherrif who's chasing after them, then lives happily ever after drinking tequila on the beach.
The narrator of the song "The Night the Lights Went Out in Georgia" by Vicki Lawrence.
I See You Baby by Groove Armada has a music video to match the title: a creepy voyeur has set up video cameras in both the men and women's bathrooms and is watching them. They find the cameras, but after a panic attack he makes a getaway with no implication he'll get caught.
Dr. Dre's "Forget About Dre":
And when the cops came through Me and Dre stood next to a burnt down house Wit a can full of gas and a hand full of matches And still weren't found out (right here)
The narrator of Warren Zevon's "Mr. Bad Example" always manages to hop a plane out of the country before the consequences of his scams catch up with him.
I bought a first class ticket on Malaysian Air And landed in Sri Lanka none the worse for wear I'm thinking of retiring from all my dirty deals I'll see you in the next life, wake me up for meals
Jay-Z, who constantly bragged on many rap songs how he made a fortune from a huge drug deal back in 1988. Supposedly, the money from this deal helped launch his rap career. Of course, it could all be unrealistic bragging which is one of the key elements in Gangsta Rap music. Then again...
"I Fought the Law" by Dead Kennedys tells the story of Dan White killing George Moscone and Harvey Milk, and only serving five years on manslaughter.
The law don't mean shit if you've got the right friends That's how this country's run Twinkies are the best friends I ever had I fought the law and I won I fought the law and I won
Maxwell Edison, the eponymous Villain Protagonist of The Beatles song Maxwell's Silver Hammer, uses his silver hammer to kill a girl named Joan, his teacher, and the judge at his trial with the implication that he got off scot-free for the murders he committed.
The narrator of Robbie Fulks's "I Told Her Lies" reaches the end of his life having never been caught cheating on his wife and considered a paragon of fidelity and loyalty in his community. We never learn how he fares against a higher authority.
The Ozzy Osbourne song "Mr. Tinkertrain" is about a pedophile who gets away with his actions.
The very last line of "Junta" by Cormorant notes that the soldiers who fired upon a huge amount of protesters will likely escape justice.
"Sold as a Crow" is about one of the MK Ultra tests, poisoning the water of Pont-Saint-Esprit.
The (thoroughly NSFW, and Nausea and Nightmare Fuel-laden) music video for "Skinless", by the band Skinless, ends with the video's Villain Protagonist, the deranged Serial Killer known as the Hudson Skinner, completely escaping capture or even exposure for his grisly crimes (one of which forms the bulk of the music video). He pulls this off by framing the members of Skinless for the murders - all the instrumentalistsnote guitarists Noah Carpenter and Dave Matthews, bassist Joe Keyser and drummer Bob Beaulac get arrested while the vocalistnote Sherwood Webber narrowly escapes capture due to being in a completely different statenote in reference to Webber's real-life residence in Denver, while the other band members live in upstate New York but is driven underground. In fairness, though, the band is thoroughly complicit in the crimes of the Skinner, and are seen performing "for" the victim in the video.