If it is a thread that you have asked to be notified when a new post is added, then just open that thread and hit the NOTIFY button and it will ask if you really want to remove it from your notify list.
If you do as I do when I first get on the computer and that is hit "show unread posts since last visit", then all I do is read those threads I am interested in and then hit "show unread posts since last visit" again and if there are no new ones, I then hit "mark all posts are read".
Hope that makes sense
Cheers
Mike