Shakespeare: Well, duh. My mom has always been a big fan of Franco Zeffirelli's films, and so I was watching Shakespearean films before I'd even begun kindergarten (especially his brilliant adaptation of Romeo and Juliet, which is my mother's favorite film). As a result, Shakespeare's language never intimidated me. By the time I began reading his plays, his vocabulary, cadences, and subject matter were all very familiar and made as much sense as anything written by a modern playwright. There's nothing I can say about his plays that hasn't been said before. They're good. My favorites are Twelfth Night (though I hate how Malvolio is abused) and King Lear. I try to attend the local Free Shakespeare In The Park each summer, and go to the Oregon Shakespeare Festival every year that I have the money to do so (it's been a few years since I went).
Tom Stoppard: Perhaps most popularly known for his movie writing (including Shakespeare In Love and Brazil), Tom Stoppard is also an excellent playwright. He's written such amazing plays as Rosencrantz and Guildenstern Are Dead, Arcadia, Indian Ink, and The Invention of Love. I've seen several of his plays performed, including Rough Crossing, which is a masterpiece of comic timing if executed well. Stoppard likes to play with intellectual subjects to make them personal. His plays are not for the faint of heart -- since many of them require quite a bit of thought in order to fully appreciate them -- but if you're willing to do your share of the work it can be an amazing experience. Tom Stoppard is far and away my favorite modern playwright. No one else comes even close.
Brian Friel: Best known for his highly successful play Dancing at Lughnasa, which was made into a film, the Irish playwright Friel has written quite a few other plays, as well. My favorite of his plays (of what I've read thus far) is Translations, which plays with language and communication in fascinating ways, while also exploring cultural imperialism. If you're interested in language and how it changes, how it affects people in concrete ways, I highly recommend reading (or seeing) this play. Friel has a lot of very interesting ideas, and communicates them in interesting ways.
Caryl Churchill: I've read a few of her plays and seen one (Cloud Nine) produced, and I love her to pieces. Though her plays were written in the 70s and early 80s, they don't feel dated to me. She explores issues of gender, sex, and politics in ways that still feel important and accurate. Cloud Nine could have been written today, and would still seem cutting-edge.
Mary Zimmerman: After seeing her dramatic interpretation of Ovid's Metamorphoses at Berkeley Rep, I was absolutely overwhelmed. If one of her productions is ever in town again, I will run -- not walk -- to see it. I can't recommend her highly enough. Nor can I imagine that reading one of her plays would even begin to do it justice. She works very closely in collaboration with her cast, giving each production an intimate and dynamic feel which just wouldn't come across in writing. If you get a chance to see one of her plays, go!
David Henry Hwang: Best known for his Tony-award-winning play M. Butterfly (which was also interpreted into a film which I never saw), Hwang is another playwright who works to communicate complicated ideas through theatre. M. Butterfly deals with issues of cultural imperialism, gender imperialism, definitions of Other-ness, and much more. After seeing it performed for the first time, I found myself continuing to think about the ideas in M. Butterfly for days (perhaps weeks) afterward. Hwang hasn't written very many plays thus far, but my reaction to M. Butterfly was strong enough that I have to list him as one of my favorites.
I should give an honorable mention to Tony Kurshner. His plays are a bit too traumatic for me to list him as a favorite, but his recent Homebody/Kabul blew my mind.
And I really should write about Oscar Wilde, because he's one of my all-time favorites, but I've become too hungry and must venture out for food. Perhaps another time.