Any way to sort a list of forums by activity?

[CarCdr]

You would have to modify the behavior of index.php to accomplish this. The delivered index.php just list them in the display order defined in AdminCP, with no option to change that behavior.

The order used in index.php comes from the array $iforumcache, which is built in the function cache_ordered_forums (you will see that call in index.php) by walking the unordered $forumcache. Each entry in $forumcache is assigned to $iforumcache as follows (stylized, not real PHP):

$iforumcache[PARENTID][DISPLAYORDER][FORUMID] = FORUM_FROM_FORUMCACHE

So, you could build the $iforumcache for index.php using your sort order, changing the DISPLAYORDER level to reflect an order based on recent activity, the 'lastpost' time stamp field from the 'forum' table.