Regarding registering purchased software, there's several reasons:
Did you lose your installation CD? If you are registered, then the company's tech support can send a replacement CD to you. Or did you lose your original download link/file? Support can email to your registered address a new download link.
Companies dont want to waste support resources supporting pirated copies of their software. For direct support, particularly when its something involved, they'll want to ensure you're a legitimate owner of the software.
Upgrades. Companies often want to provide discounts to previous customers for things like upgrades and/or companion products. They can send discount codes to registered owners.
And of course, there's the practical matter of marketing. When a new product is released, or a new version available, they want to let you know so that you might buy it.
What I really hate is companies requiring you to register just to use a trial or free version. But then, thats why they invented GMail... so we all can have throwaway email addresses.