Yep, there's enough material out there for a two-parter. (If you missed part I, it's here.) I should mention that above all others, one band takes the grand prize for serial killer songs -- the Japanese metal group Church of Misery, who in 10+ albums, have rarely written a song not about a serial killer. Here's a sampling of their work, about California serial killer Ed Kemper:
Gary Gilmore: The Police, "Bring on the Night"
This spree killer was famously written about in Norman Mailer's The Executioner's Song. Killed by firing squad in California in 1977, he accepted his death sentence and fought hard against the ACLU and other groups working to grant him stays of execution. He was so impatient, he even attempted suicide twice in prison. The Police's song doesn't reference Gilmore directly, but the theme fits him like a glove.
Columbine killers: Chumbawumba, "We Don't Want to Sing Along"
Another song filled with veiled references, the usually upbeat Chumbawumba surprises with this song about school bullying leading to tragedy.
Charles Whitman: Harry Chapin, "Sniper"
Whitman was the psycho who killed 14 and wounded 32 in a shooting rampage at the University of Texas in 1966. Harry Chapin penned an emotional song about the incident.
Charles Whitman: Insane Clown Posse, "The Tower"
A considerably less nuanced song about the same incident. Warning: this video is a bit graphic and probably NSFW. (What else would you expect from the Posse?)
Charlie Starkweather: Bruce Springsteen, "Nebraska"
Charlie was a spree killer who shot 11 people in Nebraska and Wyoming during a roadtrip with his young girlfriend in 1958, immortalized in one of my favorite movies, Badlands. Bruce Springsteen also wrote this song about it, from the album of the same title, Nebraska.
Jack the Ripper: Nick Cave
There are lots of songs about Jack the Ripper, but I prefer Nick Cave's take on the killer.
Pretty Boy Floyd: Woody Guthrie
Floyd was more bank robber than murderer, but he did his share of killing along the way, too.
Ted Bundy: Jane's Addiction, "Ted, Just Admit It"
The message of this song is pretty clear from the title, I think. Though the lyrics are a bit vague, including some weird gems like "I am the killer of people / You look like a meatball."