Scenes: the opening fight, Juliet/Maria's betrothal to Paris/Chino, Juliet's debut party=Maria's first dance, the balcony scene=the fire escape scene, Romeo & Juliet's elopement (The Friar corresponds to Doc)= Tony and Maria acting out a wedding, Tybalt/Bernado killing Mercutio/Riff, Romeo/Tony killing Tybalt/Bernado, the Nurse being taunted and insulted by the Montagues and thus unable to tell Romeo that Juliet's death is faked=Anita being assaulted by the Jets and thus lying about Maria's death, leading to Romeo/Tony's suicidal response.
Jerome Robbins explicitly set out to produce a musical version of Romeo and Juliet set in contemporary times, so it's hardly surprising that there are such parallels.
Utopia, Ltd. features a Sir Edward Corcoran, KGB, who can be identified with Captain Corcoran of H.M.S. Pinafore—especially given that he sings part of the younger character's entrance song. Since Corcoran and Ralph Rackstraw switch places at the end of the earlier musical, it is a matter of some debate which of the two (if either) the older character is supposed to be.
Part of the reason for the many examples in the plays of William Shakespeare may be that he wrote most of his plays for the same actors, leading to plenty of Actor Allusion.
An Epileptic Trees theory has argued that the Antonio of Twelfth Night is the same as the Antonio of The Merchant of Venice. Both seem to be homosexual and it's argued that the character of the former, who is a sea captain, was able to become a wealthy merchant thanks to help from Sebastian and Viola.
Iachimo from Cymbeline has a name essentially meaning "little Iago" and has a similar role in manipulating a character to wrongly suspect his love interest of cheating. The difference (fitting the names) is that while Iago is a really evil Diabolical Mastermind, Iachimo is an Inefectual Sympathetic Villain.
The Merchant of Venice has Launcelot (technically Launcelet, "little Launce"), an obvious copy of Launce. Both characters are oddball servants who go off into comedic monologues, and their dialogues and jokes are eerily similar. Nerissa could also be seen as the new and improved Lucetta—both are maidservants who act as straight men in practically the same dialogue about suitors, and both assist their mistresses in disguising themselves as boys.
Plot outline: Guy A and Girl A are in love. Girl A's father doesn't want them to be together. Meanwhile, Guy B tries to catch Girl A but is continually rebuffed. Girl B, who Guy B dumped in favor of Girl A, lurks in the wings, feeling sorry for herself. In the end, Guy B changes his mind, he and Girl B get back together, and everyone's happy. Now decide for yourself whether you want these four to be called Valentine, Sylvia, Proteus and Julia or Lysander, Hermia, Demetrius and Helena. It doesn't really matter.
The basic "Friar Laurence" type appears a third time as "Friar Francis" in Much Ado About Nothing, once again convincing people that the best solution to any romantic difficulty is for the girl to fake her own death.