There is a setting in the INI file: bAllowScreenShot=0

change it to: bAllowScreenShot=1

Also, two related items for the screenshots:

iScreenShotIndex=0
SScreenShotBaseName=Oblivion

There are two INI files, one in the game folder called "Oblivion_default.ini", this is the one it uses to generate the real one:

My Documents\My Games\Oblivion\Oblivion.ini

Edit the first one if you want to default to having screenshots on by default for all users. The settings it uses at runtime are the ones from My Documents folder.

After you edited the INI file, you can press PRTSCN button and Oblivion will write a BMP file to your game folder.