Oberon and Titania quarrel in II i 60-145. Ostensibly their disagreement is about the Indian boy, and their quarrel is resolved when Titania gives Oberon his way and lets him take the boy.
Jealousy is an equally important theme in their relationship, though. Titania's first words to her husband accuse him of "versing love/To amorous Phillida" and of being Hippolyta's lover. Oberon replies in kind, accusing Titania of loving Theseus and of having made Theseus break faith with at least four women.
Through the fairy king and queens jealous bickering we also learn of Theseus and Hippolyta's erotic histories. So both the rulers of the fairy world and of the humans' world are promiscuous. This contrasts with Hermia's maidenly concerns that Lysander lie too close to her. Theseus and Hippolyta are somewhat apart from the rigid rules of Elizabethan sexuality that are practiced in Shakespeare's version of Athens. This can be seen as related to their status as mythic characters placed into a realistic though fictional world, but also to their untouchable roles as rulers. [link to something about Elizabeth?]
Another interesting point is that Oberon's jealousy is quenched by seeing Titania with another man, but a man who is a monster and in an affair that is orchestrated by Oberon (IV i 1-79).