In order of how they appear in the film:
SAM: I don't think Gandalf meant for us to come this way.
MAUHUR: What do you smell?
EOMER: How long has it been since Saruman bought you?
GRISHNAK: Ooh, they look tasty.
UGLUK: Looks like meat's back on the menu, boys!
FRODO: I do not ask you to come with me, Sam.
GANDALF: Your fingers would remember their old strength better if they grasped your sword.
SAM: You can't take your eyes off it. I've seen you.
GOLLUM: Give it to usss raw...and wriggling!
FRODO: This creature is bound to me. And I to him.
FARAMIR: A chance for Faramir, captain of Gondor, to show his quality.
LEGOLAS: That is no orc horn.
GIMLI: You could have picked a better spot.
LEGOLAS: Your friends are with you, Aragorn.
GIMLI: Let’s hope they last the night.
GIMLI: I’ll have no pointy-ear outscoring me!
PIPPIN: It’s too big for us.
GIMLI: Toss me. Don't tell the elf. [That has GOT to be the most obvious one of all.]
TREEBEARD: Hold on, little Shirelings. I always like going south. [I'm going to hell for that one. But it cracks me up.]
FRODO: I can't do this, Sam.
SAM: I know. It's all wrong.
...There were several that I considered, but ended up cutting because they were just a tad too subtle ("Frodo wouldn't have got far without Sam") or repetitive (countless times Gollum says "Come, hobbits, come"--would've gotten lame very shortly).
Can be updated and edited once we get a proper transcript. This one, upon closer inspection, is still missing bits. But still a valuable and worthwhile achievement.