Cain and Abel are dreams that embody the characters in the Biblical story of the same name: the first murderer and the first victim – and so Cain is constantly killing his brother Abel, who never stays dead.
Cain and Abel are polar opposites: where Cain, the older brother, is cruel, sadistic, and short-tempered, Abel, the younger brother, is neurotic, gentle, and fearful of everything, most of all Cain himself. Cain torments Abel nonstop, and when not bullying, frequently kills Abel in a macabre form of obsessive-compulsive disorder; whereupon Abel revives, with the frequent hope for a more harmonious relationship based upon the brotherly love he craves: "...two brothers and they love each other very much, and they were always nice to each other. And the elder brother would never hurt the younger brother. Never."
Though the pair often function as comic relief in a dark way, it is they who shelter Dream upon his return to the Dreaming until his strength is restored, following his imprisonment in the waking world.
In Season of Mists, Cain was chosen as Dream's emissary to Hell, as he was the only denizen of the Dreaming who could return without being destroyed by Lucifer: "You may not hurt him. We may not give you our permission. Cain is under the protection of One far greater than the Lord of Dreams."
While Cain is easily infuriated by Abel, dialogue between the two suggests that Cain does genuinely care about his brother, but is unable to stop killing him. After Abel was murdered by the Furies who were laying waste to the Dreaming, in The Wake, Cain pleads to the new Dream to revive his brother, which he does.
Cain owned a large green gargoyle named Gregory, and in Sandman, issue #2, Cain gave Abel an egg that soon hatched into a golden gargoyle. Abel named the gargoyle Irving, but Cain insisted - with violence - that the names of gargoyles must always begin with a G. Abel, after another death and resurrection, prudently renamed the gargoyle Goldie, after an invisible/imaginary friend to whom Abel told his early House of Secrets stories, "but I will think of you as Irving really."