Yes, we should still read Shakespeare. The stories are entertaining and make you think. They also have been around so long that they are almost universally known. Many modern books, movies and television shows still do regularly allude to them.
I always tell my students that while they may not be able to relate directly to the situation of a Shakespearan play's plot line, they should be able to relate to it undeniably. That is why we should still read Shakespeare's plays. I use the example of Hamlet. While I should hope that not one of my students will be visited by the ghost of his or her dead father and told to do something he or she don't really find to be in his or her nature, I would say that every one of those students will be faced with the choice of action and inaction and will face Hamlet's dilemma of "To be or not to be" in the context of action vs. inaction. They will all have to decide what the "nobler" path is, and recognize that sometimes "conscience makes cowards of us all." From the same play, I hope they come to realize that "there is a Divinity that shapes our ends, rough hew them how we will." There are SO many gems of pure truth in Shakespeare, I can't imagine a time when it would be deemed that his plays, and therefore his themes, are unnecessary.
Shakespeare is one prime example of timelessness. His stories are relevant and entertaining centuries after he wrote them, and he reminds us that literature is also art, as is the language itself.
Sure, there are some examples of stories and authors that have managed to stay in the curriculum out of sheer tradition, and I wouldn't mind their being phased out in favor of other works, but Shakespeare, I hope his work is permanently in our schools and our libraries.
I think it's still important to know Shakespeare's plays because they are part of our cultural legacy. When people have some knowledge of lots of Shakespeare's plays, it binds us together. Shakespeare's plays are also quite good at making us think about various dilemmas that come with being human. That is one of the major reasons for reading literature and Shakespeare is particularly good at this.
I think that it would be better if we could read the plays in modern English, though. There is no need for us to read most of it in an archaic and hard-to-understand language. Some stuff ought o still be read in the original for the poetry of it, but most of it need not be. After all, people who speak foreign languages read Shakespeare in their own languages and still get something from it.
So I think it is still relatively important to know the most famous of Shakespeare's works. However, I think that the plays would be better if we were allowed to read them in our modern language.
The answer is simply, 'Yes.'
William Shakespeare penetrated human understanding with such beauty and accuracy that his work is immortal. Not all students will 'get it', but it is a lifeline for the intelligent and sensitive readers.
"I say there is no darkness but ignorance." W.S.