First we see him in the scenes above.
Then we see him in the staircase scene where Nute Gunray orders the Queen and her people processessed (it is here he orders Threepio to encourage the Queen to sign the treaty and not to leave her until she does he takes these orders literally).
When Qui-Gon and Obi-Wan are about to storm the hanger (remove Pananka's line "They need her to sign a treaty to make this invasion of theirs legal." to something similar by Threepio (I can't stand the way Hugh Quarshie delivers most of his lines in TPM anyway, he is a good actor but I understand he wasn't having a happy time making that film".
He is placed with the Queen in most shots and becomes a warning voice for her (or her decoys) always reminding her of the odds against her.
When the Queen and her crew get onto the ship Threepio comes too. and sticks with whoever is wearing the Royal wardrobe until the battle breaks out in the palace at the end.
He can't climb up to the upper levels and is captured before Padme but is brought into the throne room to translate.
When Padme seizes the Viceroy Gunray points to a gun on the floor and orders Threepio to shoot the Queen.
He strongly advices Gunray not to put his life in further danger (thus reminding Gunray about the odds against him) and tells him that assassination is not permitted by his programming.
Padme keeps Threepio as her part of the heavy reparations the Trade Federation have to pay Naboo.
For AOTC he stays on Naboo most of the time in the service of the Queen but when Anakin decides to return to Tatooine Threepio comes along too he pops out for a few minutes to let them know they have a message from Obi-Wan (that way Owen hasn't owned by proxy Threepio for months but has seen him for a few minutes, which explains how he wouldn't twig twentyish years later who he is until Luke mentions Obi-Wan, up until then he was just another droid).
In the droid factory he still loses his head but doesn't get the head swap or enter the arena, Artoo repairs him in the factory and switches off the security systems to allow the Jedi to sneak into the arena with relative ease.
Threepio and R2 attend the wedding (he is gold in all of these scenes).
Threepio is in all the restored deleted scenes in ROTS.