When I thought shock Albee's The Goat occurred to me. It not so much a thriller but it's psychological and there are some interesting twists and shocks. The other play that I remember is The Dying Gaul by Craig Lucas. It's three characters and the play watches as they twist and change before us. It also has some internet/online chat scenes that would probably be fun to play with.
I would seriously second Anthony Shaffer's "Murderer" for it's breath-taking opening and seriously...fourth Ira Levin's "Veronica's Room". That one is an evil little chiller of a play.
There's another overlooked thriller from the '60's called "The Playroom" by Mary Can't-remember-her-last-name about a group of spoilled/misunderstood wealthy kids who fake a kidnapping. The original kids on Broadway included Karen Black, Richard Thomas and Christopher Norris.
You might want to try to find a copy of "Children,Children" a thriller in which Gwen Verdon made her non-musical stage debut about a baby-sitter getting psychologically terrorized by the children she is watching. It closed on opening night.
"A coherent existance after so many years of muddle" - Desiree' Armfelt, A Little Night Music
"Life keeps happening everyday, Say Yes" - 70, Girls, 70
"Life is what you do while you're waiting to die" - Zorba
Equus would be good, as someone mentioned. My first thought was the Crucible. But I think a really good one would be Buried Child. There is some really dark humor, but it's very heavy and has some good twists.
"This table, he is over one hundred years old. If I could, I would take an old gramophone needle and run it along the surface of the wood. To hear the music of the voices. All that was said." - Doug Wright, I Am My Own Wife