I wasn't sure what these were used for and thought some were just left overs from previous games, but the staff at The Cutting Room Floor have the answer! Observe:
Norimaro has an unused attack, or possibly a taunt, where he thinks about a girl from the Capcom side and he then has a massive nosebleed. The blood can damage the opponent. There are also sprites for Chun-Li and Zangief which fit inside his thought bubble.
Norimaro has an unused animation where he looks down, then gets down and looks ahead. felineki has suggested that this would have been used as a win pose if he'd beaten Sakura, so he could look up her skirt. I'd go with that idea, especially since he has a special intro animation with her.
Norimaro is not playable in the USA and European versions of the game, but he was clearly meant to be as his special moves which had kanji in them were translated into English. See here for more info.
Here is a bizzare one: Karin Kanzuki! She wouldn't debut until 1998 in Street Fighter Alpha 3, a year after this game came out. It seems some work had been started on her sprite though, and it also seems she was originally just going to be a swap of Sakura with a different head and boots instead of sneakers. Thanks to Ragey for the GIF.
Dhalsim's wife from Street Fighter Alpha 2 is still in this game, with all of her animations.
Sakura's shinkuu hadouken fireball from Alpha 2 is also in there, with all necessary animation.
Apocalypse has another unused attack, which apparently wasn't finished -one of his hands turns into a pincer which slowly moves towards the opponent and can push them back. His other unused attack from X-Men Vs. Street Fighter is also still in this.
Omega Red: "Your life force stinks!"
Omega Red: "Never!"
Omega Red: "Omega Strike!" and "Omega Destroyer!" -these were originally used in X-Men: Children of the Atom.
Originally, Norimaro was going to have a Kancho attack which basically involved him shoving his fingers up his opponent's bottom (Click here for more info on Kancho). It looks like this move was going to be a throw, but it was removed from the game completely (the sprites for it were taken out) allegedly because Marvel got really angry about it and bluntly damanded for Capcom to get rid of it. Thanks to rickcressen for uploading this clip which shows it.
This is from a Japanese flyer for the arcade version. I have never seen this screen in the game.
Scratch that, Ta-Cheng Lee got in contact with me and said that that screen is actually in the game, and provided me with a screenshot.