Gollum/Smeagol say their own personal catchphrases from the films during their acceptance speech. When he appears and snatches the award, Gollum calls Andy Serkis "a liar and a thief" and brags, "It's mine! I won it... It was me! We only won because of me!" When it is Smeagol's turn, Smeagol says, "MTV is My friend... My friend!" Gollum responds by saying, "You don't have any friends! Nobody likes you!" Gollum says 'My Precious" when he is lambasting Peter Jackson for being a hack. After Gollum curses a blue streak, Smeagol moans, "Not listening. I'm not listening." Gollum also refers to himself as "we", which is a trademark phrase from Gollum's speech pattern.
After Gollum's show-stealing acceptance speech, the camera cuts back to Elijah Wood. If you read his lips you can see he's saying "That was f***in' awesome!". This can also be seen in The Lord of the Rings: The Two Towers (2002) Special Extended Edition DVD as an Easter Egg bonus, See Trivia of The Lord of the Rings: The Two Towers (2002)
The Gollum acceptance speech won the 2004 Hugo Award for Best Dramatic Presentation, Short Form, controversially beating out episodes of Firefly, Buffy the Vampire Slayer, and Smallville.
According to Peter Jackson on the Lord of the Rings Two Towers DVD, Fran Walsh and Phillipa Boyens wrote the Gollum MTV award skit.
Gollum says "My Precious" one time, "f----" seven times, and "MTV" three times.