William Shakespeare's plays may be centuries old, but their popularity has never waned. There are a number of reasons for this. First, according to Professor Craven of the University of Texas, Shakespeare's plays deal with themes like "love, treachery, honor and bravery," which are still relevant today and, therefore, resonate with modern audiences. (See the first reference link.)
In addition, Shakespeare was an innovator when it came to language. He invented many words and phrases which are still in use today, like "new-fangled" and "scuffle." As such, Shakespeare's creativity makes for enjoyable reading, which is another reason why he remains so popular.
Finally, many of Shakespeare's plays have been adapted and turned into new plays and films. One example is the film 10 Things I Hate About You, which is based on Shakespeare's play The Taming of the Shrew. This movie introduced his comedy to a new generation of readers, further ensuring its enduring popularity.
For more information, please see the second reference link provided.