This play has stood the test of time, because in its many variations, it is a timeless tale of two people who want to be together, but shouldn't be or can't. People fall in love every day, and lots of those couples face seemingly insurmountable odds -- distance, social class, family obligations, prejudice, etc. that keep them apart. They may wish they had the strength to be together no matter what the odds or the costs, but most don't. Say what you will about the veracity of Romeo and Juliet's feelings, they DO do everything to be together -- something lots of people can't say, but can admire.
Shakespeare's plays have withstood the test of time because of their universal themes. In Romeo and Juliet, you have the ever-popular tale of two young lovers who naively believe that their love can overcome the harsh realities of the world around them. Shakespeare gives us two loving, yet feuding families, and a group of young, hot-headed males ready to stoke the fires of war. He then adds the comic characters of the Friar and Nurse, whose attempts to assist the young lovers directly result in their death. And then you have the clincher: a tragic ending in which the feud dissolves only after the death of the young lovers. Change the setting and the language, and you have a modern blockbuster. We read and study Shakespeare today because we can relate to the characters and the themes hundreds of years after he wrote them.
One reason Shakespeare's play Romeo and Juliet still resonates with high school students is the fact that the lovers themselves are teenagers. Also, their impulsiveness is a character trait that most teenagers can relate to. Over the course of five days, Romeo and Juliet meet, fall in love, get married, and kill themselves. That's all it takes. It takes only five days. Teenagers can certainly relate to the intense feelings that Romeo and Juliet felt for each other. Whether those feelings were love or lust is up for debate.
Romeo and Juliet also has a bit of the supernatural with the potion that Juliet uses to fake her death. This type of mysticism is the same thing that attracts young readres to the Harry Potter and Twilight series.
Finally, Romeo and Juliet also adds an exciting element of violence that teenagers are typically intrigued by. It makes for a great play to act out in class, when swords are brought in as props and students can out out the several duals throughout the play.
A lot of people think that "Romeo & Juliet" is the classic love story, but there is so much more to it that every interpretation can take on a life of its own. Eventually, any reader can see that love is actually a very low priority. Family feuding, escalating violence, and mistaken identity are much more substantial to the play. Even religion and social norms are more important than two teenagers who fall into lust.