Ovid, Metamorphoses: Transformation in the play; the source of the characters Pyramus and Thisbe.
Chaucer, The Knight's Tale:Hippolyta and Theseus are characters in this tale. Also, Lysander and Demetrius's pursuit of Helena echoes the way two knights, Palamon and Arcite, fight over Emily.
Plutarch, Lives of the Noble Grecians and Romans: Plutarch's "Life of Theseus" informs Shakespeare's portrayal of this character.
Apuleius, Golden Ass: This seems to be the literary source for Bottom's transformation into a human with the head of a donkey
Corinthians 1: 2-9: Bottom's language in 4.1 is a parody of St. Paul's Epistle to the Corinthians.
Elizabethan Political Figures
Queen Elizabeth I: Oberon's description of the "fair vestal [virgin] throned by the west" (2.1) is a shout-out to Shakespeare virgin monarch. Also, "Fairy Queen" (Titania) was Queen Elizabeth's nickname.
Figures from Folklore and Mythology
Hercules (1.2, 4.1, 5.1)
Diana (1.1; 1.1); as Phoebe (4.1)
Cupid (1.1, 1.1, 2.1, 3.2, 3.2, 4.1)
Venus (1.1, 3.2, 3.2)
Robin Goodfellow is often referred to as Puck and sometimes called "Hobgoblin." He's a common figure in English folklore.