It's only appropriate, in my opinion, when it's scripted in. For instance, the entrance of the Emcee in Cabaret or the entrance of Hedwig in Hedwig and the Angry Inch allow for applause. The entrance of Chita in The Visit should get no applause, because it doesn't make sense. As others have said, including the actors/actresses themselves, it messes with them getting into character convincingly.
BROADWAY: The Cripple of Inishmaan, This is Our Youth, If/Then, Hedwig and the Angry Inch (x3), Cabaret (x2), The Real Thing, A Gentleman's Guide to Love and Murder, Chicago, Les Miserables (x2) Disgraced, Finding Neverland, On the Twentieth Century, Wolf Hall Part I, On the Town, Fun Home; TOURING: Jekyll and Hyde, The Book of Mormon; LOCAL: The Twilight Zone, Anne Boleyn, Death and the Maiden, The Lying Kind, Chorus Line, Stupid F**king Bird