My favourite straight play (as in not a musical; not just plays that only have straight characters! Although these two probably do only have straight characters...) is a toss-up between Who's Afraid of Virginia Woolf? by Edward Albee and Long Day's Journey Into Night by Eugene O'Neill. Both have been adapted into films, both have about four main characters and both have as their underlying conceit plenty of alcohol and yelling at one another! If only drama could be boiled down into such a simple equation: alcohol + raised voices = theatrical dynamite! If I had to choose between them, I'd probably go for Virginia Woolf. If you'd asked me that a year or so ago, the position would probably be reversed, but after having seen an amazing production last year on Broadway (which ended up winning the Drama Revival Tony) it's gone up significantly in my estimations.
As for favourite musical, I'd have to go with Company by Stephen Sondheim. I'm a big Sondheim nut, liking pretty much all of the major stuff he's done (except West Side Story, but that's a debate for another time). For me, Company has the edge partially because it was the first one I saw, but also because all of the songs are so enduring, the book so bitter and acerbic in the way that most musicals fear to go down, and the depths of character it reveals astonishing.