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.