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.
http://www.youtube.com/watch?v=YSO6dQClEYs&feature=channel_video_title
Lots taken out from DH1, Krum, extended Scrimgeour scene, Harry finding Lily's Letter (!!), Ron's growing tension, and I'm sure there's more
*None of these videos are mine, credit sportsman893 on YouTube for finding all of this