Of the three traditional genres—epic, lyric, and dramatic—we have no record of any “epic” or prose writing (short stories, novels, essays). Most Shakespeare anthologies identify the dramatic genres Tragedies, Comedies, Romances, and Histories. His lyric genres include, of course, sonnets, and, according to the Riverside introduction to Venus and Adonis “Ovidian mythological-erotic” poems. The Rape of Lucrece, very popular in Shakespeare’s time, was in the genre called the “complaint poem.” The Phoenix and the Turtle is sometimes called “a poetical essay”, but here the word “essay” means “to try.”
As for his dramatic subgenres, while Shakespeare may have bits and pieces in these categories, no full-length play of his can be called a farce, a religious pageant, a folk play (like Gammer Gurton's Needle), or the modern genres such as an absurdist play, a family drama (although some of his plays might be considered them), or a “black comedy.” It was not till King James’ reign that bloody (later called Grand Guignol) dramas were allowed on stage.