Advanced Forum adds some functionality to the core forum module by itself but, to really emulate stand alone forum software, you need more modules. Many of the modules here are automatically integrated into Advanced Forum, most by way of the Author Pane module which is a requirement.
This page starts you off with suggested modules but you'll also want to visit the community category in the downloads section for more ideas as new modules are constantly being added. You could also see Drupal modules equivalent to phpBB features.
Enhanced user information and interaction
Profile (core)
Flag Friend or User Relationships (Buddylist on D5)
PrivateMsg
User Points
User Badges
User Stats
User Titles
Imagecache Profiles
Facebook-style Statuses
Ignore User
Author pane
Content entry
BUEditor or wysiwyg
Live
Quote
Smileys
Signatures for Forums
Comment Upload
Forum Moderation
modr8
Abuse
Comment Mover
Re: Comment subjects
Administration, and Utility
Forum Access
Fast Toggle
Flatcomments (Forces all replies to be against the node to avoid deleting issues with hidden threading.)
Edit Limit Enables setting of a time limit for editing original posts (nodes) and replies (comments).
Misc
Subscriptions or Notifications or Comment Notify or Comment RSS