There are two main types:
1. Freudian/Psychoanalytic Criticism
-Oedipal complex, libido, id, ego, superego, subconscious, repression, resistance
-Harold Bloom: strong-poet theory (authors subconsciously react to predecessors)
2. Archetype/Myth Criticism
-"collective unconscious" revealed through archetypes
-some overlap with Formalism & Structuralism
-Jung; James G. Frazier, The Golden Bough; Joseph Campbell; Northrop Frye
For more information, I recommend Culler's Literary Theory: A Very Short Introduction