The 'My Posts' and 'All Activity' sections of my chow are automatically generated based on your recent use of the site. You can't clear them out, but there is a limited number of them, so they will eventually fall off the bottom of the list as they age and you participate in additional threads.
You can remove items from your 'Favorites' by clicking the small 'X's
Items on your 'Reading List' are generated based on the activity of people you've added. You can remove people from your list, which will take all their contributions with them, but not individual posts.