Romeo and Juliet
Above anything and everything else, West Side Story is a retelling of Romeo and Juliet. There's lots of reasons to watch this film, but the genius adaptation of Shakespeare's tale of star-cross'd lovers is the big one.
The similarities are obvious: lovers come together from two sides of a bitter conflict, overseen by an authority figure who can't seem to do a darn thing about it, and it ultimately costs the couple their lives. The lovers meet at a dance; it's obsessive love at first sight; a balcony scene; fights in the street; people close to the main characters get killed; and in the end, the two would cheerfully commit suicide if it meant going through life without the other. You could totally write a killer English essay about all the parallels.
You can even spot specific characters patterned after each other. Just change the feuding Montagues and Capulets to Jets and Sharks. Tony is Romeo, Maria's Juliet, Riff's the best friend Mercutio, Bernardo is Tybalt… it goes on and on. The dialogue's modern (though the songs are performed in meter, like William Shakespeare wrote) and the setting is contemporary (though it may not feel that way now since it came out over half a century ago).
But in every way that counts, it's Romeo and Juliet.