Should I register my new Apple products with Apple? Apple asks to register products in the installation but I am unsure whether this is a good decision. If I sell the Apple -products later, does it cause some problems? What is the point of registration?
Once you've completed the registration, all the information you've filled up, will be sent to Apple with your iDevice / Computer's Serial Number. 

Having an Apple Id associated to a Device is necessary for the AppleCare Protection Plan, but, if you purchased the AppleCare at the same time as your Device / Computer, the Protection Plan will be automatically registered, being unnecessary for you to do so.

The information you fulfill and submit is useful in other ways, using Autofill in Safari, for instance, or enable the possibilty of using the Remind me of-doing-something when I get Home of the iPhone 4S. 

Therefore, if you want to sell your Mac or iDevice, you could just make a clean install to get rid of all that info. Not deleting it will just cause privacy / security issues.