Go into the "Show new replies" or "Show unread posts" tab next to your avatar photo/name. Once there, click the checkbox to the right of the topics you no longer wish to see. Then click the "Ignore topics" button at the top or bottom of the list.
If you don't see the checkboxes, go to Profile/Modify profile/Look and layout, and select "Show quick moderation as checkboxes"
You can unignore topics in the Modify profile/"Ignore topics options" section.
Devlyn
