None of my apps are keeping a list of recent documents? Example:

If I open an image in Preview, the "File/Open Recent" menu lists the name of the file.
If I then close the file, but still leave Preview running, the "Open Recent" menu still lists the file.
If I quit Preview, the "Show Recents" menu does not show any files.
If I reopen Preview, the "Open Recent" menu does not show any files.  



I have a feeling this is a permissions problem, but repair permissions has not helped.

In Console, Preview is reporting the following error upon opening:

"29/02/2012 14:45:57.183 com.apple.Preview.TrustedBookmarksService: Failure to de-serialize bookmark data file."

I'm using Preview as an example here, but it holds for every app - whether they are bundled or downloaded - on my system.

System Preferences/Appearance/Number of Recent Items is set to 10.

I am running Lion 10.7.3 on an iMac 12,1 with a dual SSD and HDD internal drive setup.
I would trash your preview .plist file located at:

~/Library/Preferences/com.apple.Preview.plist


Restart Preview, and it should create a new one.  It sounds corrupted.