The following are things that can enhance your Drupal Forum. What has been discussed so far will make the forum seem a lot like phpBB, but still have some things missing. Here, we'll try to fill in the gaps.
More enhancements may be found here: http://drupal.org/node/227121. I don't plan on implementing everything, so you may want to browse this list to see what, if anything, suits your needs.
This is the wysiwyg editor that I use. There are others available, so take your pick.
UPDATE: I have switched to using the WYSIWYG editor in combination with WYSIWYG Image Upload. WYSIWYG is great, and allows you to easily install various editors. WYSIWYG Image Upload is nice, if it works. Unfortunately, it doesn't work in conjunction with Facebook Connect, so until this gets fixed (the problem is probably in Facebook Connect) I'd recommend using this at your own risk (though, it is the most intuitive image upload tool I have found for Drupal.)
The User Stats module allows for showing user information, such as join date, post count, etc. Install as usual, then go to Administer -> Site Configuration -> User Stats settings to edit according to you needs (you might want to include the forum topic in the post count.) This will expose the statistics to the theme developer to place in the post.
The user image in the forum posts will typically be fairly small (say, 100x100 pixels.) When you go to the user's profile, it would be nice to have a larger picture so we can better see who this person is. This is where ImageCache Profiles comes in.
Install the module and its prerequisites (ImageCache). The Readme file contains a good overview of how to implement this, but here's the basics:
Maybe some members have a tendency to ramble on about pointless nonsense. Install the Ignore User module and members can choose to ignore the posts of others.
Installing the Quote module will place a 'quote' button so that users may include the original post in replies. Install the module, then go to Administer -> Site Configuration -> Input Formats. Configure the Forum input format to include the Quote filter. You will also probably need to rearrange the filters (click the rearrange tab at the top) so that Quote comes before line-breaking filters and BBCode. Next, go to Administer -> Site Configuration -> Quote and check the forum topic. Make sure 'Display the quote link for nodes' is checked.