Most everything else I would mention has already been posted, but read The Normal Heart. Seriously, read it or you fail.
I know, broken record, flashback to 2004. Just read it. And read The Destiny of Me while you're at it.
Others yet to be mentioned:
Stoppard's Arcadia, Rock 'n Roll, The Real Thing
Sarah Ruhl's eurydice, and for something a little bit weirder, Dead Man's Cell Phone
Anything Tony Kushner has written ever. Even "bad" Kushner is worth reading.
Bennett's The History Boys
Lucas' Reckless
Lindsay-Abaire's Rabbit Hole
A work of art is an invitation to love.