I recently directed Dario Fo's "Abducting Diana". It went well and was a lot of fun to do. I'd recommend it, along with Fo's "Accidental Death of an Anarchist".

I'd also recommend Paula Vogel's "How I Learned to Drive" and anything by Steven Dietz.

No one has yet mentioned Three Viewings - this is a wonderful script that has a dramatic edge to it, but also very funny.  A real crowd pleaser. 

Also, I would recommend looking at Line.  This is very weird, very edgy, and your audiences will leave saying, "What the hell was that?"

Down the Road by Lee Blessing is edgy - about a serial killer and a couple who is writing a book about him.

And I would second votes for Stop Kiss.

There's a version of Electra that was written in the 40's, some french fellow.  I know I sound like a fool or something, but it's edgey, but in that subtle sort of way, I mean, you know, incest is pretty edgy. 

There's also The Laramie Project, and while Moises Kauffman's work is usually just him masturbating on stage... it's an amazing, amazing, amazing piece of approachable theatre.

Wit is edgey, having done it myself, I'd LOVE LOVE LOVE to design that play again, with probably one of the strongest scripts I've come across in a long time. 

I think many great "edgy" plays started, or ran only, Off-Broadway.  Slab Boys (with Kevin Bacon/Sean Penn), American Buffalo (with Al Pacino), Sam Shepard's True West, Extremities (with Karen Allen).