I have often times wanted to write something like CheckBoxList1.Items.Where(i => i.Selected).  Turns out you can't do that, because the Items property is a "specialized" collection.  But to get it to work all you have to do is cast it to a generic list of ListItems like this:

var selectedItems = CheckBoxList1.Items.Cast<ListItem>().Where(i => i.Selected)

The example above uses method syntax, but you could also use query syntac like this:

var selectedItems = from i in CheckBoxList1.Items.Cast<ListItem>()
                    where i.Selected
                    select i;