"The Elder Scrolls IV: Oblivion" for the PC has multiple official updates that fix bugs and improve the game's stability. Knowing which version you have tells you which updates, if any, you still need to install. It's also helpful in determining which mods are compatible with your version of "Oblivion."
Oblivion's Main Menu
"Oblivion's" main menu lists the version number in the lower left corner. If you've installed any mods that change the user interface, your main menu may be different.
Oblivion Install Directory
Navigate to "Oblivion's" install directory, which is in your Program Files folder by default. Open "OblivionLauncher.exe" and click the "Technical Support" option. The version installed is listed under the game's name in the "Read Me" tab. You can also find the version number within "Oblivion's" install directory by right-clicking "Oblivion.exe" and selecting "Properties." Navigate to the "Details" tab to find the version under "File Version."
As of November 2014, Steam offers no option to check a game's version within the Steam client. By default, Steam automatically updates games. "Oblivion" players will still be able to see their game's version number from the game's main menu.