When the Von Trapp kids play catch with the baroness, the baroness gets hit in the crotch with a ball.
"Reverend Mother, I have sinned..."
After the Captain asks Maria why she still has her dress if all her clothes were given to the poor: "The poor didn't want this one..."
In the same scene: "Were you this much trouble at the Abbey?" "Oh, much more, sir."
Also, "I won't have to whistle for them, Reverend Captain—I mean—"
"I am not finished yet!" "Oh yes YOU ARE, CAPTAIN... Fraulein."
"...and THESE... are my children."
"Fraulein, is it to be at every meal, or merely at dinnertime, that you intend on leading us all through this rare and wonderful new world of... indigestion?" "Oh, they're all right, Captain. They're just happy..." (cue mass bawling)
Kurt asking Brigitta not to call Maria's dress the ugliest one they ever saw, since one of their previous governesses wore an even uglier one.
"Will father approve of this?" "Of course [...] Don't you trust me?" "No." "Smart girl."
"So long! Farewell! Au revoir! Auf wiedersehn!" "I'd like to stay and taste my first champagne! Yes?" "No." Followed by what can only be described as a :( on Liesl's face.
It comes to her later: "KURT! That's the one I left out! God bless Kurt!" *BOOM*
Speaking of Kurt, when he introduces himself as "incorrigible", Maria responds with "Congratulations"...which is funnier when you realise what incorrigible actually means. (meaning uncontrollable or firmly fixed in their ways)
Maria stops in the middle of her own musical number when she sees the size of the house. Julie Andrews's delivery of "Oh help" is priceless.
After Liesl casually mentions that Louisa can make the climb up to the governess' room with a whole jar of spiders in her hand, Maria reacts brilliantly. And despite having a heart-to-heart with Liesl, she spends the rest of the scene sneakily checking under her bed clothes for anything. She jumps when she does find something... but it turns out to be a slipper.
Somewhat "meta" here, but hearing the nuns complain about Maria "singing in the abbey" becomes about five times funnier when you realise that the nuns are singing in the abbey.
Brigitta's blunt honesty throughout the film is priceless.
When the children and Maria discuss who should sing next, Maria then presents her guitar to the Captain. The look on his face is utterly priceless.