Here are my views on these:
A New Hope:
The Search for Artoo
Alternate Luke and Biggs Reunion (Would have given some depth to Luke's backstory as well as that of Garven Dreis)
Extended conference room scene (Involves General Tagge referring to Vader as a "Sith Lord", would have added depth to the way the Imperials fear him.
Garouf LaFoe reporting the altercation in the Cantina to Stormtroopers (Could tell us why the Stormtroopers would attack the Millennium Falcon)
Extended Alderaan destruction (Leia has more of a reaction here)
The Empire Strikes Back:
C-3PO setting Wampas on Snowtroopers
Luke's lightsaber training
Leia tells Luke about Han Solo's capture
Snowtroopers manning an E-Web blaster (Would've been cool to see Snowtroopers in action)
Return of the Jedi:
Luke building his green lightsaber (would have provided some depth)
Rebel Raid on the Bunker
Moff Jerjerrod turning the Death Star to destroy Endor (When the shield generator was destroyed, the Empire was pretty much screwed. Also the destruction of the moon would have destroyed much of the rebel fleet and Palpatine could come back with the Final Order and crush everything anyways)
Yoda revealing to Luke that he had forbade Obi-Wan from telling Luke that Darth Vader was his father.
Additional shots of B-wings destroying a Star Destroyer
The Phantom Menace:
Anakin's Scuffle with Greedo
A Naboo soldier showing Padme that the battle droids have been deactivated
Anakin flies his N-1 Starfighter back into the hangar
Bail Antilles of Alderaan
Additional dialogue with Darth Maul (Fear is my ally)
Attack of the Clones:
Padme addresses the Senate
Obi-Wan and Mace on the Jedi Temple landing platform
Padme's parents' house
Dooku interrogates Padme
Anakin and Padme on Trial (These scenes would have given information to their execution)
The Lost Twenty
Raid on the Droid Control Ship and Extended Arena Fight (Would make sense that the battle droids were now independent of their control ships)
Dooku fighting with Obi-Wan's lightsaber as well as his own
Revenge of the Sith:
Extended space battle (Would be cool to see Anakin and Obi doing some dogfighting)
Anakin and Obi-Wan fight Dooku as a team (Covered by a video from Star Wars Analyst)
Palpatine presenting changes to end the war to Anakin
Rebel Alliance subplot (These scenes would have made ROTS a lot more political but on the flip side, they would have revealed insight on how the Rebellion was formed)
Anakin talks with Palpy about Obi-Wan's mission to Utapau
Obi-Wan selects Boga from a Varactyl Pen
Anakin killing Shaak Ti
Anakin throwing lava at Obi-Wan during their fight. (Shows how Anakin became a lot more powerful since his turn to the Dark Side)
More coming soon! (Add your ideas below)