'Purchase Error', 'Unexpected Error', 'Invalid key' or 'Duplicate key' reported when activating Steam keys

If Steam reports either an "Unexpected" or "Purchase" error when you attempt to activate a key (as shown in the example screens below) 

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Check you have the latest available version of the Steam client using the "Steam, Check for Steam Client Updates..." menu.

Then, try logging out of and back into Steam (allowing Steam to update, if necessary), check if the game is the already listed in your library and if not try activating the key again.