The character of Crowley in Good Omens has obviously either read The Screwtape Letters or else was at Tempters' College being taught by Screwtape. Crowley's realisation that the world is too big for craftmsmanship and that "you can't pick the buggers off one by one any more" as there are far too many of them is a restating of Screwtape's maxim - get the leaders and the herd will follow. The bureaucratic nature of Crowley's Hell — and, by extension, Aziraphile's Heaven — is also straight out of Screwtape.
U2 singer Bono is a big fan of the book, and his devilish MacPhisto stage persona is inspired in part by Screwtape.
In the video for "Hold Me, Thrill Me, Kiss Me, Kill Me," an animated Bono is holding a copy of the book just before he gets hit by a car. In a new animated video for the song that was played during the band's 2018 Experience + Innocence tour, band members are greeted by a shadowy man with a business card reading "Wormwood & MacPhisto Inc. Bespoke Atonement Services."
The album Dear Wormwood by The Oh Hellos was partially inspired by the book.