Avatars - I can almost guarantee that this is going to rank high on everyone's list considering it's been one of the most talked about subjects since the new forum came up.
Attachments - I don't think a lot of people have fully taken advantage of this feature yet, but I think it's awesome. In case you don't know when you add a new thread or post a reply you have the option of adding an attachment to it down below.
Embedding video - I don't think this was available on the old forum because I never saw it done, but people are definitely starting to take advantage of it here on the new forum. Of course, my connection here sucks, so I don't get to use it as much as I like, but it's still pretty cool.
Downloadable PMs - Again I don't think this was possible on the old forum, but it has definitely come in handy on this new forum. Now when ever my PM box gets full I just download everything, so I can reference the files later.
And Finally My Personal Favorite...
Friend's List - I love this feature. I use it to keep track of people's who's posts I liked, that I talk to a lot, or that I bought really cool WSOs from. It makes it way easier to keep track of the people you talk to the most instead of trying to do a search for them every time you want to send them a message.
Anyway, I'm sure I missed plenty of the new features, so feel free to add your own. And if you have used all the features that I posted, I recommend you check them out.