Some companies, depending on your job and tasks, will require your SSN. For example, if you are given access to a company credit card they will require you (not always) to give them your SSN, so that they can continually check your credit. They do this so they know they can trust you to use the card wisely.
Not sure where you are getting your info Spec but it is NOT illegal to ask for a SSN. Trust me I know, I am in the military and it gets thrown around on everything. It is even on my ID card.
And not to mention that they need it to set up your taxes.