After the credits, we hear Lecter say "Ta ta, H.", the closing line of the post-script in his letter to Clarice.
After fading to black, the alternate ending features a new voiceover-- Hannibal: Clarice, would you ever say to me, "Stop. If you really love me you'll stop?" Clarice: Not in a thousand years. Hannibal: Not in a thousand years? That's my girl.
As the opening credits end, Hannibal's face can be seen in the formation of pigeons on the ground before they fly away.