Hi,
Now you mention it, part of this behaviour started for me in Mountain Lion. I went straight from Snow Leopard to ML without trying Lion, and I only had ML for a few months before I went to Mavericks. In ML, I recall, the folders I left open on the dock stopped reopening on startup, but the other behaviour (folders left open on the desktop not reopening but files and apps I had closed or quit reopening) proliferated in ML.
"Close windows when quitting an application" was checked by default, but rechecking it seems to stop closed and quit files and apps from opening most of the time. However, when I do open an app like Word by clicking on one existing file, for a while all the recent files opened, which they didn't used to do on current settings, and lately this has changed to the project gallery and a new blank file opening automatically. But sometimes it just goes back to everything in every app I used last time opening, and sometimes only the file I want to open does open.
Meanwhile, I usually have "reopen windows when logging back in" checked so that the folders I left open will reopen. As I said, this never works for folders left on the dock anymore. Folders left open on the desktop vary. If I uncheck and recheck the "reopen windows" control during shutdown it behaves itself for a while, then I find that only one folder of a group left open is reopened, then none.
Settings should not be able to wear off. Thanks to all who offered help, but this inconsistent behaviour indicates a bug, rather than that users haven't understood the settings. We've all been using these settings for years. It seems a small irritation but it is very annoying for something that used to work well to stop working, particularly if it interrupts your workflow. I'll report it to Apple again.