If you mean the notification if you click on "You have X new replies to posts"... No, unfortunately you can't. You can, however, ignore the entire board the thread is located in. To do so, go to your profile and select Ignore boards option in the Modify profile dropdown menu. If someone makes a post in a thread you posted in that is also located in a board you ignore, the number X no longer goes up. However, you can still find new posts for that thread back there if you click on it.