Well here of some of the songs I correlate to some of my favorite dc characters.
Batcat/Batman and Catwoman: Under your scars by Godsmack, Dancing in the Dark Bruce Springsteen (via the Brave and the bold number 197) Hurt by the Nine-inch Nails as covered by Jonny Cash.
Batman: The Vengeful One Disturbed, Land of confusion (Genesis and covered by Disturbed) Monster When my Devil Rises MAN WITH A MISSION (ok it’s about the Japanese superhero Devilman but it fits Batman too) The Touch by Stan bush what you gonna do, Hinder, I Stand Alone Godsmack, Batman Theme songs.
Catwoman, Harley Quin, Poison Ivy: Bad girls world Halstorme, Bat Romans Gotham City Sirens.
superman and Lois lane: Waiting on Superman Daughtry
Superman: superman theme song
Wonder woman: the wonder woman theme song from the 1975 tv show.
The Flash: Flash by Queen(ya its about flash Gordan but it works) The flash theme
Jona Hex Vigilante (justice league cartoon): I Should Have Been a Cowboy Toby Keith