Stephen Sondheim's Into the Woods spends its first act as simply a retelling of the stories of "Jack and the Beanstalk", "Little Red Riding Hood", "Rapunzel", and "Cinderella", all tied together with the story of a baker and his wife who are cursed with infertility unless they can procure certain items from all four. In the end it looks like everyone's gotten what they want and is happy, but suddenly the narrator announces "To be continued!" Act two begins with the idea that the giant was just minding his own business when Jack came up the beanstalk and killed him, and just builds from there into an incredibly brutal Anyone Can Die deconstruction of fairy tales.
Hamlet has been read as a massive deconstruction of Elizabethan revenge dramas. Although most of them end in tears for everyone, Hamlet deconstructs the genre by having the characters react to events like the ghost's appearance like a real person would (in a standard revenge play, the appearance of a vengeful ghost was an expected part of the genre, but Hamlet doubts the ghost's reality for half the play, as a real person who saw a ghost probably would).
Measure for Measure might do the same for comedies. The whole thing is a source of much debate.
Romeo and Juliet can be read as a deconstruction of the idea that "Love at First Sight" can exist, since Romeo and Juliet's attraction is interpreted by many readers as purely superficial, more to do with lust than love, and brings nothing but tragedy to everyone around them (and, of course, themselves). Again, it's debatable.
Romeo And Juliet has also, with some success, been interpreted as a genre deconstruction of Commedia dell'Arte. The stock characters are nearly all there, and the Star-Crossed Lovers plot, the Zany Scheme... only this time the zany scheme works just as well as an overly elaborate plot to get two teenagers together can be expected to and a lot of people die.
In a like manner, Titus Andronicus can be read as a Deconstruction (or even a Satire) of revenge dramas. The over-the-top blood and gore, and the obvious mental instability of everyone, including the play's purported "heroes," have led some modern audiences to call this play the most "Tarantino-esque" of Shakespeare's works.
A Streetcar Named Desire did not deconstruct any genre in particular, but it did deconstruct gender roles, physical relationships, and the American system of social classes in a rather harsh way.
Older Than Feudalism: Euripides' Trojan Women and Hecuba portrayed The Trojan War as a human tragedy rather than a sweeping epic tale of martial valor in the Homeric tradition. In general, his tragedies are regarded as more "modern" than those of his predecessors because of their morally ambiguous protagonists, pervasive sense of anxiety and despair, religious skepticism and overall portrayal of mythologycal subjects and characters as real people.
Urinetown deconstructs a typical Dystopia story. It has downtrodden people fighting to overthrow the oppressive system that heavily taxes and regulates their bathroom usage during a worldwide massive drought. They succeed, but they are so caught up in the "freedom" that they don't control themselves at all and end up squandering all the remaining water.