If you have posted on a thread, it will continue to show up when you click "show new replies to your posts." What I do is to read all the new posts I want to and just click the "mark all messages as read" button when I'm done. That will remove the unwanted threads, until a new post is made on them.
If you don't need to post, but do want to follow a thread, then click "notify" on the right at the top of the posts. That will give you notices when new posts are made. And you can undo it if you want to stop following the thread.
Many people do post on a thread just to make sure they get updates. It works, but the "notify" button does the same thing and gives you the option of cancelling the notifications if you want to.