There are several instances in A Midsummer Night's Dream in which the characters wake up believing they have had a strange dream when in reality they were actually under a spell. Two of those instances can be seen with respect to the characters Titania and Bottom.
When Oberon releases Titania from the love spell using a flower called "Dian's bud" as the antidote, Titania awakes as if she had been in a dream the whole time. "Dian's bud" serves as an antidote to the spell cast by Cupid's flower because Diane is a goddess that is celebrated for her chastity. Chastity is the exact opposite of being in love, so it serves as an antidote. When Titania awakes, her first comments are, "My Oberon! What visions have I seen! / Methought I was enamour'd of an ass," as if her whole experience with Bottom had been a vision or a dream (IV.i.75-76). When Oberon shows her Bottom, still with the donkey's head on, Titania realizes how much she hates the vision of the donkey now. Not only that, since the spell served to help Oberon obtain the Indian boy he was jealous of, Titania and Oberon have now stopped fighting and are friends once again, as we see in Oberon's line, "Now thou and I are new in amity" (87). Hence, the result of the spell for Titania, which she thought was a dream, was to trick her into releasing what was separating her from her husband.
A second instance of a character being enchanted but thinking that he/she is waking from a dream can be seen in Bottom. When Bottom awakes, he believes he has had a dream that is beyond mankind's understanding, as we see in his lines, "I have had a most rare vision. I have had a dream, past the wit of man to say what dream it was" (IV.i.208-209). He decides to tell Peter Quince to write a sonnet about his vision that he can sing before the duke after their play. Somehow, though, Bottom's vision of himself as a donkey has turned him into a far more humble character than he was before. We see his humility when in the very next scene, after deciding to tell the whole world about his dream, he decides to keep silent. When his friends ask him to tell the story, all he says is, "Not a word of me" (IV.ii.30). Hence, we see that as a result of the dream, Bottom has learned humility.