I usually delete a book from my reader when I'm finished with it.
But if you want to keep your read books on your reader, you could create a "read" and an "unread" collection on your reader. You'll need to hook your reader up to your computer to drag the books to and from the proper collections though. Also you can't "nest" collections, so if you're already using collections you won't be able to look for a book in for example "science fiction" & "read" at the same time.
Hope this helps--