You mean left out as in it wouldn't also be in the EE?
And from how I understood your question, you're just asking us what were our favorite parts in the book that was left out in the movie, you're not asking us what parts of the book do we regret that they were left out in the movie? Because I think it's different.
First of, it's like this. I liked the Scouring of the Shire because it was awesome in the books, but I NEVER regretted it that it was left out in the movies because I know that it was unnecessary basing from how the movies were made. I wasn't pissed off with that.
I also loved the scenes in the Barrow-downs and Tom Bombadil but I wasn't really pissed that they weren't in the movie. Reason? Look above.
Eowyn and Faramir. If they had been left out in the EE, I will regret it terribly. They are my favorite literary couple and I was very touched by their story, more so than Arwen's and Aragorn's, but since we're not talking about love stories here, I'll just shut up about it and not prolong the issue anymore. Anyway, we haven't heard anything about the scene yet. We know it was filmed, but nothing is heard if it will be put in the EE or not.
Hhmh..for some reason, Fatty Bolger fascinates me, so he's of my left-out favorites, along with Prince Imrahil.
Halbarad and the other Dunedain Rangers, they're very awesome and cool. I just regret it that if they had managed to put some Elves in Helm's Deep even though it NEVER happened in the book, how come they haven't managed to put in the Dunedain Rangers if they actually appeared in the book?
I heard Bergil will be in the EE, someone was casted as him, but if it wasn't put in, then he's one also.
MoS and VoS were confirmed to be in the EE, so I wouldn't consider them left out.