Given the general nature of this question, I will keep it in the literature group where it presently resides.
This is an interesting question, because many people actually believe that Shakespeare's plays are the creation of somebody else apart from Shakespeare, or at least the result of a collaboration between Shakespeare and another dramatist, such as Christopher Marlowe. Also, at the time of Shakespeare, it is interesting to note that the plays of Marlowe were actually considered to be superior to Shakespeare's work. Some critics today still argue that Marlowe is the better dramatist, and that we should be studying Marlowe instead of Shakespeare. I have included some links below to give you more information about Marlowe, but certainly his plays, including the great Doctor Faustus and also Edward II and Tamburlane the Great are certainly excellent.
If you are after a more modern day playwright, I would personally like to suggest Arthur Miller as being somebody whose plays at least approach equality in terms of greatness. He has managed to create modern day triumps such as The Crucible and Death of a Salesman that have captured the spirit of an age and also raise timeless themes such as the individual vs. society and personal guilt and the importance of reputation.