Most companies require a social security number and a few an EIN number, or a choice between the two. More companies are requiring you to fill out a W-9. On the W-9 you have the option of entering a SS# or a EIN#.
Despite what some people may think, as a shopper you are in business for yourself. We require a w-9 to be on file for all shoppers, period (Our clients require us to have a W-9 on file). If we ever get audited we want a record on who we compensate. We can show the IRS who we compensate, their address and SS# (or EIN). And yes, they can follow up to see if you reported the income on your return. It is a part of doing business. Remember, even if you make $10 from any one company you must report that as income.
Personally with all the ID theft going on I would prefer to give out my EIN number rather than my SS#.