If you have a lot of books on your Kindle, you already know how cumbersome slogging through all those "pages" of books listed on your home screen. And some times it just helps to take inventory and weed out the ones you don't want taking up Kindle space.
Hook your Kindle up to your computer with the handy dandy USB cable. Open your Calibre software and watch for the menu buttons to reflect your Kindle being connected. You will see a Library and Device button side by side.
Right click (or Control click if you have a mac) and choose Remove books to remove any selected book from your Kindle.
Don't worry about removing books you purchased from Amazon (free or otherwise). These books, even when removed from your Kindle will always be available in your Amazon Archives, unless you delete them for good in the manage your Kindle area of your Amazon account.
I love using Calibre to organize books on my Kindle. I use it for my iPhone and iPad book organizing too. It just works! You can download the latest version at http://calibre-ebook.com/.