Technically, your receipt is all you need to prove you bought the product, when and where. So legally, you do not have to register your product to activate the warranty and obtain warranty support. But registering can make getting support faster since the purchase will be on record. That can be a lifesaver if you lose your receipt.
Registration also gets you on their list for notifications in the case of product recalls, or of new driver and firmware updates.
So in your case, with your mouse and keyboard, those are pretty low-tech, reliable products Windows already knows how to use. Your printer, depending on its features, may be worth registering.
HOWEVER! Submitting your warranty information is also a good way to get on spamming... err... mailing lists. So when/if you do register, make sure you read everything carefully and "opt-out" of any and all email notifications that have nothing to do with that specific piece of hardware. And never provide information they don't need. For example, they don't need your phone number, your age, your gender, or your annual income.