List of alternate/deleted scenes, arranged in chronological order:

Deathtroopers surveying the area while standing in front of the Erso home, which is on fire (Teaser Trailer)
alternate shot of a Rebel soldier asking Jyn if she “wants to get out of here” in the Imperial transport on Wobani (Trailer #2)
Jyn being marched through a hallway in the Yavin 4 base in handcuffs, and looking behind her before a guard pushes her along (Teaser Trailer); the final film has a similar shot, but she walks through the hangar bay, doesn’t look behind her and no one pushes her
General Draven’s line “Can you be trusted without your handcuffs?” (Teaser Trailer)
Mon Mothma’s line “On your own, from the age of 15, reckless, aggressive and undisciplined” (Teaser Trailer)
Jyn’s line “This is a Rebellion, isn’t it? I rebel.” (Teaser Trailer); appears to have been changed to the single line “You’re Rebels, aren’t you?”
Jyn’s line “I was trained to fight, not stand down.” (TV spot #14)
Jyn/Draven’s exchange at the end of the briefing scene (“Is that clear?” “Yes, sir.”) (Teaser Trailer)
the shot of the Star Destroyer passing the Death Star’s reactor dish as it retracts is different (extended out further, moves in more slowly) (Teaser Trailer)
unused scene/shot of Jyn pausing to give something (a piece of fruit?) to the young girl she later saves during the Jedha Stormtrooper/tank fight (Celebration Teaser Reel)
unused scene of Jyn/K-2S0 talking in Jedha(“You are a friend. The captain says that I should not kill you.” “Thanks.”) (Trailer #1)
alternate/unused shot of Jyn/K-2S0 encountering Stormtroopers harrassing residents in Jedha (“Jyn & Cassian” extended TV spot)
the shot of present-day Saw Gerrara in his base walking towards the camera, still bald like his earlier appearance in the film (Teaser Trailer)
Present-day Saw Gerrara (sans hair) asking “What will you do if you fight?” (Teaser Trailer)
quick shot of Jyn talking to Saw outside of his Jedha base (Celebration Teaser Reel)
footage from alternate scene of Krennic talking to Vader inside Death Star (“The power we are dealing with here is immeasurable!”) (Trailer #2)
unused shot of Krennic saying “The power we’re dealing with is… awesome.” (TV spot #29/IMAX TV spot)
alternate shot of Jyn telling Cassian “I’m not used to sticking around when things go bad” before departing for Scarif (“Jyn & Cassian” extended TV spot)
alternate/unfinished shot of Jyn telling the Rebels “May the Force Be With Us” before leaving Yavin 4 (Celebration Teaser Reel)
unused shot of Jyn telling the Rebels “Welcome to Rogue One” before leaving Yavin 4 (“Tonight” TV spot)
unused Bodhi line “You might want to strap in” before the Imperial shuttle heads for Scarif (TV spot #37)
unused shot of X-Wings departing Yavin to head to Scarif (“Father” extended TV spot)
Jyn (sporting a rifle in each hand) and other Rebels running towards a group of AT-ATs who are firing on them (Teaser Trailer)
Jyn, Cassian and K-2S0 running through a hallway in the Scarif base without their disguises (Teaser Trailer)
unused shot of Jyn in disguise (sans helmet) turning back to stare at something in Scarif base (various trailers/TV spots)
Jyn walking to the Scarif Tower’s alignment console as a TIE Fighter rises up in front of her (various trailers/TV spots)
shot of Jyn/Cassian running through gunfire and explosions during Scarif ground battle (Celebration Teaser Reel); notable in that Jyn is holding the Death Star data drive in her hand
shot of Jyn/Cassian and other Rebels behind a dirt barricade laying down blaster rifle fire on Scarif surface (Celebration Teaser Reel)
Krennic walking through shallow water on Scarif(?), with his robe trailing behind him (Teaser Trailer)
Vader looking at a projection screen in the Death Star (Trailer #1)

It is noticeable that a large chunk of Saw Gerrara’s scenes were reshot (see the trailer scenes of him on Jedha with no hair, versus his appearance in the final film), at least one Vader scene was changed (it appeared he would have been on the Death Star and had a similar conversation with Krennic), and the ending was massively reshot so that part or all of it involved Jyn, Cassian and other Rebels escaping on foot instead of transmitting the data via the satellite dish on Scarif Tower).

I had also heard a rumor prior to release that the original ending was supposed to be Jyn/Cassian escaping the surface with the plans, but they’re killed anyway when Vader disables the flagship and and boards it.