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.
This might be averted with follow-up song "The Hazards of Love Pt. 3", in which the spirits of the titular rake's murdered children return to exact revenge on their father.
Flower of the Plateau, in which Mikulia 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.
Death Metal. No Seriously. Gore related songs never reveal that the murders getting any comeuppance. Each and every song ends with the killer continuing his crimes.
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.
"Karma Chameleon" by Culture Club.
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...