Play (Male): Jefferson Mays, I Am My Own Wife Play (Female): Cherry Jones, Doubt
Female in a play was incredibly hard. Actually the only one where I had a true definitive answer was Actor in a musical (although I thought of two other people).
For now, I'm actually going to cast my vote for Jefferson Mays in I Am My Own Wife.
Man, this thread certainly reflects the current demographics around here.
Without question, my answer is Christine Ebersole in Grey Gardens. I have never, nor do I believe I ever will again, see as thorough and complete a transformation as this one. The level of nuances she brought to these roles have been unmatched.
I remember seeing A Streetcar Named Desire at BAM, with Cate Blanchett as Blanche, and thinking to myself after it was over "Well I never need to see that again. No one could possibly do it better."
And just because drama always seems to take precedent over comedy in discussions like these, James Corden's comic genius in One Man, Two Guvnors cannot be overstated.
Glenda Jackson in “Three Tall Women” and Carey Mulligan in “The Seagull” immediately come to mind. Also feel very strongly about Harriet Walter and Janet McTeer in “Mary Stuart”.
Natasha Richardson in "Cabaret." Faye Dunaway in "Master Class" Michael Crawford in "The Phantom of The Opera" Elaine Paige in "Sunset Blvd" and "Piaf"
Jefferson Mays in I Am My Own Wife. The play and production on Broadway were phenomenal. Mays felt effortless in all his character transformations done right in front of the audience and managed to draw focus from an extremely intricate set design of floor to ceiling living room sets ups with slight variants stacked behind him. My eye did not wander from him when he was onstage.
I've only been a regular theatregoer for a few years so I don't have many contenders, but that performance left me completely drained. In the best way. It's either her or Andrew Garfield in ANGELS IN AMERICA.