Jim Morrison has been used in comics on several occasions but primarily through autobiographical comics or small roles relating to his real life persona being a part of the comic's respective world.
Major Story Arcs
Shade, the Changing Man
A rare example of Jim Morrison being involved with a semi-mainstream character was in Shade, the Changing Man #40 written by Peter Milligan (who is known for showing his love of bands of that era in comics such as The Sex Pistols). In the story, a nerdy kid named Nigel who hangs around with his friends at Morrison's grave suddenly gets the urge to touch the gravestone and becomes possessed by Jim Morrison.
Jim ends up at Hotel Shade where he meets Shade himself (who has no idea who Jim is being an alien and all) who seems about to embark on an another weird adventure of his own and invites Jim to come along. Morrison has no problem getting right back into his alcoholism of old but finds disappointingly the kid's body can't hold its liquor.
Jim seems to find the whole thing (including Shade's powers) to be one fun adventure and wants to continue the party elsewhere but Shade is out to ease his own guilt (as well as that of a man named Tony Muller they come to meet who has painted the same design that mysteriously formed on Shade's abdomen).
The man it turns out was a Jim Morrison look-alike in the sixties who was even hired by Jim himself to lure away fans once and the guilt he is living with is that he took advantage of a teenage girl back then by claiming to be Morrison. When he is told that the nerdy kid accompany Shade is Jim himself back from the dead, he merely laughs it off.
The three of them go to seek out this girl, Sadie McKay, and find her in a hospital bed after she had been in an automobile accident. Upon entering the room Jim tells Shade that this is definitely the voice that had been calling him back from the grave. Tony tries to wake her up but it doesn't seem to work so Jim tries to sing and manages to sing a small portion of "Break on Through (To the Other Side)". His voice remained intact through the possession as Tony realizes it really is Jim and Sadie wakes up to see Tony (who she assumes did the singing) and thinks Jim has come back for her after all these decades.
He confesses the truth of their meet-up and so Tony and Sadie begin to rekindle their relationship (brief as it had been) and forget all about the now-ugly Jim and Shade. Jim seems upset his singing bringing the girl out unconsciousness got him nothing and asks the question of whether anybody would want him lighting their fire had he not been so attractive.
Dissatisfied with the scrawny, acne-ridden body he's been sentenced to, Jim decides he's going back to his grave in France. Upon returning to the gravestone, he turns to Nigel's friends who are still hanging around (listening to "Love Me Two Times") and asks them to turn the music off as it really starts to grate after awhile. Then he touches the tombstone and returns to his afterlife.
In 2000AD #559, during an interlude story of the ongoing Zenith serial, the back-story of a group of seven super beings called "Task Force UK" is shared and the members briefly named and shown. Although most of them don't receive a direct link between their name, powers and appearance; one is quite clearly meant to be Jim Morrison and is referred to as Lux. While the character's date of death isn't directly stated, the teammate to die before him died in 1969 and it is said the members all met their fates within a few years (the real Morrison having died in 1971). He is claimed to have died when "his body's chemical structure inexplicably disintegrated".