To turn off the display off all signatures in a forum, open any thread in the forum, then click the "turn signatures off in this forum" link located at the top right of the forum display page.
This will prevent the display of all signatures in the current thread AND in all threads you view from that point on for that particular forum. If you want to turn them back on, simply click the "turn signatures on in this forum" link at the top right.
To turn off your own signature in a post or in all posts you make to a particular forum, please see this wiki.