Is there a way to make Preview not open all previously opened files?

Solution 1:

This is part of resume. A feature introduced with Lion.

Per default, windows are restored the next time you open the application. If you want to completly close all windows just one time, you can quit an application using ⌘+⌥+Q instead of the standard ⌘+Q to quit an application.

Undo resume for a specific application

Type the following command in the Terminal. Then restart the specific application.

In general the syntax is:

defaults write com."producer"."program-name" ApplePersistenceIgnoreState YES

Thus, in your case (Preview.app) it is:

defaults write com.apple.Preview ApplePersistenceIgnoreState YES

If you prefer a graphical interface, you can use TinkerTool.

This application gives you access to additional preference settings and allows to activate hidden features in the operating system.

Undo resume for all applications

In order to disable this for all applications do this:

go to System Preferences->General->Restore windows when quitting...

Solution 2:

In addition to the other answers you an also use Option ⌥ + Command ⌘ + Q when you close preview instead of Command-Q which will ensure that it does not remember which files it had open.