Among the scenes in the senate there was one involving Bail Antilles, (who obviously can't be an ancestor of Wedge because Wedge is Corellian) the Alderaanian senator. Lucas eventually deemed the scene unneccesary. There was a picture and short entry on Bail Antilles in the Episode I Who's Who book.
When Obi-Wan, Qui-Gon, and Jar Jar exited the Bongo, they were filmed swimming through a waterfall before arriving in Theed. To shorten the scene, it was taken out.
A scene was filmed where R2-D2 fell off a platform on Coruscant and used built in rocket boosters to get himslef back up.
Anakin Recites his Dream
While Anakin is showing Padmé his pod-racer, he originally told Padmé about a dream he had where she was leading an army into battle. Padmé then replied with, "I hope not, I hate fighting."
Jedi Council Discussions
In one of the Jedi Council scenes, there was a deleted shot with Yaddle, Saesae Tinn, and Even Piell talking to each other.
Anakin's Advice to Jar Jar
After Sebulba attacked Jar Jar, they cut off a few lines. Anakin said, "Fear attracts the fearful. He was trying to overcome his fear by squashing you...be less afraid." Then Padmé askes, "And that works for you?" Anakin replies with "To a point." The line Fear attracts the fearful was put into the Darth Maul TV spot as well as the music video for Duel of the Fates.
Qui-Gon Offers Food
When Anakin takes Qui-Gon into his home, a cut part of the scene included Qui-Gon taking food capsules and offering it to Shmi because he knew that being slaves, they would have a meager source of food.
Anakin Fights "Greedo"
After the pod race and before Qui-Gon takes Anakin with him, there is a cut scene where Anakin was fighting with a young Rodian. The Rodian's name was writen in the script as Greedo, but it obviously would not be able to be the Greedo from A New Hope because he was born on Rodia and raised on Nar Shaddaa. Wald is also in this scene. After the fight Qui-Gon arrives. There is some dialogue exchanged.
QUI-GON: What's this?
ANAKIN: He says I cheated.
QUI-GON: Did you?
QUI-GON: Do you still think he cheated?
QUI-GON: Well Annie, you know the truth. You will have to tolerate his opinion, fighting won't change it.
ANAKIN and QUI-GON walk away. WALD goes over to GREEDO.
WALD: Keep this up GREEDO, and you're going to come to a bad end.
Jar Jar Eats Clams
In the scene where Qui-Gon rescues Jar Jar, Jar Jar originally was supposed to be opening a clam that he had gotten from the swamp and eat it, then the MTTs would come from behind him and Qui-Gon would rescue him.
Air Taxi Scene
Another deleted scene took place after Qui-Gon tells Valorum that he needs to talk to the Jedi Council. The cut scene has them all board an air taxi and leave the landing platform.
Naboo Pilots and Anakin
After the Droid Control Ship was destroyed, Bravo Squadron originally was wondering who it was who destroyed the main reactor, and then Anakin comes and reveals himself.
BRAVO TWO: He flew into the hold behind the deflector sheld and blew the main reactor.
BRAVO THREE: Amazing, they don't teach that at the academy.
ANAKIN'S ship comes to a stop in the hanger. The pilots rush toward it.
RIC OLIÉ: We're all accounted for. Who flew that ship?
ANAKIN gets out and sees all the pilots.
ANAKIN: I'm not going to get in trouble am I?
Get Out of the Ship
When the Naboo pilots are manning their ships, Anakin was originally supposed to hide behind one of the ships. Then Celia Imrie, one of the pilots tells Anakin, "Better find a new hiding place kid, I'm taking this ship." R2-D2 then whistles to Anakin from another ship not far away.
There was a cut scene on Naboo, before Qui-Gon introduces Jar Jar to Obi-Wan, where qui-Gon is holding Obi-Wan's waterlogged saber.
OBI-WAN: Sorry, Master. The swamp fried my lightsaber.
OBI-WAN takes out his weapon and gives it to QUI-GON. QUI-GON inspects it.
QUI-GON: You forgot to turn off the power again, didn't you Obi-Wan?
OBI-WAN: It appears so, Master.
QUI-GON: It won't take long to recharge, but it will take time to clean up. I trust you have learned your lesson, my young Padawan.
OBI-WAN: Yes, Master.