If you look at the post right next to yours about
Custom columns you will see a lot of people using those to store whether they have read a book or not (as do I). Just create a Yes/No column. It is easy enough to then use that in searches and/or setup a saved search for a restriction on your library so that you will only see books that are marked as not read.
To set it up:
Preferences->Add your own columns
Click on the hyperlinked Yes/No at the top between "Modified Date" and "Tags".
Change the Lookup name to "read"
Change the Column heading to "Read"
The column type of Yes/No is what you are after.
Click Ok, restart calibre.
Now you can use the Yes/No dropdown to tick books you have read.
To search for books you have not read, in the search box you would type
#read:false (alternatively #read:no)
Save this as a saved search on the RHS by typing a name where it says "Saved Searches" and click the green +.
Then on the left hand side, you can click on the "Restrict to" dropdown to limit your view of the library to just your unread books. If you want that restriction every time you open that library, go to Preferences->Behaviour.