In System Preferences, when I try to change "Recent Items" count from "none" to any other value it is not saved. I can change it, but when I close System Preferences and open it again I still see "none" in "Recent Items". What can be the problem? Is there a way to change it manually? I am using OS X 10.11 "El Capitan".
Sounds like the .plist file is corrupted. Go to Library/Preferences and drag the file named com.apple.recentitems.plist into the Trash and empty it. When you open System Preferences again a new com.apple.recentitems.plist file will be created and you should be able to change the number of Recent Items without issue.