My favorite dramatist is Henrik Ibsen. Other playwrights whose work I like are Edmond Rostand and Terence Rattigan, and of course Shakespeare (one of these years I will get around to reading all of Shakespeare's plays). Below is a list of plays I have enjoyed reading or seeing on stage.
Aristophanes, Lysistrata -- The quintessential anti-war play -- plus it's extraordinarily funny, too!
Aphra Behn, The Rover -- This Renaissance gem is witty and intelligent and lots of fun.
Robert Bolt, A Man For All Seasons -- The tale of Sir Thomas More and his devotion to truth and his own conscience.
William Gibson, The Miracle Worker -- The inspiring story of Helen Keller's discovery of language and reality.
Lorraine Hansberry -- A Raisin in the Sun
Henrik Ibsen -- In the year 2001 I re-read all of Ibsen's prose dramas, and captured my impressions in journal entries from 2001-08-30 and 2001-11-09. Based on this re-reading, I would say my favorites among his plays are The Pillars of Society, A Doll's House, Ghosts, An Enemy of the People, The Lady from the Sea, The Master Builder, and When We Dead Awaken.
Terence Rattigan, The Winslow Boy, French Without Tears, Separate Tables, etc. -- All of Rattigan's plays are highly recommended. The main challenge can be finding them, since most are out of print (try The Advanced Book Exchange).
Edmond Rostand, Cyrano de Bergerac, Chantecler -- Romantic drama at its best.
Sophocles, Antigone -- A classic of individual integrity.