My browsing experience on DC is dominated by the Unread Posts
page, so that's vital for me. I love how clicking the "new" icon brings me to the last post I haven't read in the thread (which may be older than the last post).
I also like how I can mark threads as unread, so they'll come up on that page again. I use this frequently to answer stuff later.
Also, I like how the "new" icon works also when browsing the boards (and not only on the unread posts page).
The fact that the "unread posts" page shows those icons with "you replied to this thread", "this thread has lots of posts" and stuff like that is also useful. (And I also use a lot the "Show new replies to your posts" page, which is a subset of the "unread posts" page).
I also like the "quick reply" box, not sure if it's available everywhere. And the attachments mod.
As a moderator, I like how it's easy to ban users (3 clicks) and it deletes the spammer's when banning, I like how posts can be reported to moderators, and I like the email notifications with suspicious stuff and mod activity.
Oh, and donationcredits. Everybody loves donationcredits
(after reading the post bellow mine
+1 for search! [/edit]