Having a phone number in their system is handy for identifying purchase history and warranty. I have a landline for DSL that has no phone connected to it so I always use that number. As others have said you could always make up an easy to remember number. For me it just makes checkout easier to give them the number you let them file and you can move on. Plus they keep sending me coupons in the mail.
It's insane how much info everybody has on you. I created accounts at USPS, Fedex, and UPS for getting tracking emails. Any time I try to make a change they come back and ask me to verify who I am by asking for answers on information that is in documents regarding land, vehicle, and tax transactions you wouldn't think would be that easy to find and access. BIG BROTHER IS WATCHING! And apparently everybody else.