So, what I've found is that there are a whole bunch of scenes that were recorded, possibly scored, and were never released. Not on the Special Edition additional features, not on the Ultimate Edition DVDs. They just haven't been seen. I've found a couple videos that show evidence of the existence of these scenes, as well as a comprehensive list, compiled on COS, of what is known to have been shot, but excluded. My hope is that we one day get LOTR style full director's cuts or extended editions.
I read that Yates stated that there was roughly 45 minutes cut from the fifth film, yet the included deleted scenes only amount up to about 7 extra minutes of footage.
I'm guessing that there's a lot more cut from the first four as well as 6-8 as well, and I really hope that WB releases these scenes.
Barring the final film, which without credits fell under 2 hours, I'm assuming that 1-7 all would theoretically have near 3 hour runtimes, which the later films really need considering how much was cut out. Some of the scenes are not that relevant, and really I'd just like to see them for the sake of seeing how they were done and how they would fit into the movies. However, some of them, I believe, could certainly have enhanced the films, specifically OOTP, as there was just so much crucial information taken out.
Here's the list from COS:
http-~~-//www.youtube.com/watch?v=f9mUJTmFuZg
This is what I'm talking about. The first few aren't as significant, but there are some interesting scenes here.
From GOF, there's quite a few smaller details that would be fun to see added in, but there's also Dumbledore's explanation of Priori Incantantem, as well as Harry pondering Voldemort's return in front of a waterfall.
OOTP just has too many too mention.
http-~~-//www.youtube.com/watch?v=V-AL1SL8KHs&feature=channel_video_title
Here's some more from HBP. Some of these are featured in the deleted scenes from the DVD, but some are not.