MommyZL's hard reset fix worked for me.
Short Explanation.
Hold in the On/Off Button at the same time as the Home Screen Button for several seconds to do a Hard Reset.
Longer Explanation.
The red update badge indicating that an app update is available, when no app needs updating started to happen with my iPhone 3GS running iOS 6.1.3, owned since new and not JB.
Not sure what caused it, but I had recently deleted an app.
I simply held in the On/Off Button (sleep / wake button) located on the top right of the iPhone and the Home Button (circular button just below the screen on the front of the iPhone) at the same time and for several seconds until the iPhone turns off and begins the Hard Reset (it took approx 60 seconds on my iPhone).
The non existant update requests has not returned.