Code Generator?
 

Is there a mod for vBulletin where a user clicks link and the link generates a code for them?

For instance for a code giveaway contest, a bunch of codes are stored in the mod and everytime a user clicks a link or button, a unique code that was stored is shown to them. One unique code per user who clicks the button or link.

Is there a mod that does such a thing?

You could append the logged in user's username or userid to the end of a URL or something but I've never seen a mod to do exactly this.