Lion has a new Resume feature, that will automatically re-open documents and windows in applications as they were when the application was last quit.
Although this feature works for the most part with newer applications like InDesign 5.5 and Word 2011, your mileage may vary with older applications. This feature may also be undesirable if you quit an application with a lot of files open, as those files will be re-opened when the application is next launched.
The Resume feature can bypassed if you press the option key down when you quit the application (this will discard remembering what was open), or if you hold the shift key down while opening the application (this will ignore re-opening things). It can also be disabled all together by unchecking “Restore windows when quitting and re-opening apps” in the General system preference pane. Note: If disabled, holding the option key down when quitting will activate the Resume feature once.