Constantine's business card has an Atlanta, Georgia code - the pilot is indeed filmed and set in Atlanta. At the time that it first aired, fans could call the number to hear a voicemail left by Constantine mentioning Alec Holland, who - in the comics - would go on to become Swamp Thing.
Towards the end of the televised version of the pilot, Constantine comments that he loves The Sex Pistols. In the comics, Constantine was not a fan, and once accidentally summoned the ghost of Sid Vicious, complete with bass, and was visibly irritated by Sid's inability to play.
Furcifer, the demon Constantine defeats, takes his name from the Latin word for scoundrel. That word is thought to have inspired the name Furfur, one of the Earls of Hell according to The Lesser Key of Solomon, a 17th-century book that included a list of the demons of Hell.
The university Constantine visits is Ivy University. Ivy University is the Alma Mater of Ray Palmer (The Atom).
The computer hacker, Ritchie, first appeared in Hellblazer issue seven. As in the TV series, he was one of the Newcastle crew and a colleague of John's. However, the comic book version is English, and does not have the post-traumatic stress disorder that his TV counterpart has, nor a reliance on medication.