As of version 1.6.5 Users can tag discussion posts (not replies) with tags.

A text field shows up when creating a new discussion and tags can be added.  If they don't exist already they will be created.

The tag attribute is actually a standard select attribute and it can be managed just like any other Attribute from their tab in "Pages and Themes"

If you'd like to disable discussion tags, just remove the select attribute with the handle "discussion_post_tags".

If you would like to use the same set of tags as blog posts you can change the attribute handle of that the disucssion addon uses by defining the following constant in your config/site.php.  Example: to set it to use the 'tags' attribute you would add this line to your config/site.php file:

define('DISCUSSION_POST_TAG_HANDLE','tags');