I'll go by Villain, 3 for each (it just came to that):
Ras Al Ghul - Hard to pick, all of his stuff is equally good. I'm going to say either the training montage or when he reveals The League's past attempts at Gotham and talks to Bruce in Wayne Manor. I also really like his first appearance, especially because it sums up Batman's existence.
Scarecrow - "Lighten Up" by far. I also like his discussion with Rachel about his Asylum. "Out there he was a giant, in here only the mind can grant you power." "Do you enjoy the reversal?". The first scene with his mask is badass, too. "They screamed! And they cried! About as much as you're doing now!"
Joker - The Interrogation Scene without a doubt, especially at the point where he's gotten Batman punching him in fury and responds with laughter. The video threat was also insanely powerful the first time I saw it, and is still scary. My third would be any one of his speeches, either about scars or his final one with Batman.
Two-Face - Without a doubt the final scene of the movie. It's magic. A lot of people love to focus on Ledger's performance, but I think Eckhart did an equally good job, this scene being a testament to that. While this may count as a Joker moment, I also really like when Batman first opens the door and sees Harvey. The way Batman walks slowly towards him, knowing he's been had while Harvey yells at him angrilly.
Bane - Without a doubt the first fight with Batman. That never gets old, watching it for the first time was MAGICAL. It's so brutal, I was hoping that he'd do the scene justice, and he did even before Batman was Broken. I never expected that, but WOW. I also really enjoy his speech to Bruce about the cave, Hardy's delivery is brilliant and the dialogue is so rich "Not of your body....... of your soul." That might be my favourite scene in the movie. Bane is my favourite villain of the series, so it's hard to pick. My third would have to be when he's walking toward Batman and Catwoman on the roof-top before they jump into the bat. I often have a love-hate relationship with these villains, that's part of the fun, but this is scene in particular that struck me as effing scary. Bane was terrifying through this whole scene.
Catwoman - If she counts, I love the double cross. Nolan really did a good job of writing her and how she goes back and forth between both sides whenever it benefits her. Her initial appearance is fantastic, also. The way she seems cute, charmed by Bruce, and innocent... then in an instant switches to her normal self. Also: there's a that shot where she positions herself on the batpod to fire it.... DAYUM, that makes me feel tingly. I also really dig her dialogue with Bruce at the ball.