Almost all of them. They are required to know your tax information so they can report your earnings. I have provided SS# to over 150 companies between 2010 and now with no problems. If you object to providing a SS#, you could always get a TIN. I just use my SS#, but I have heard the TIN is easy to get.
I'm signed up with about as many as roflwofl. I have been shopping for 15 years and all of the companies I signed up with have my SS#. I personally don't like the idea of getting an EIN or TIN. Some shoppers have one and a few companies want shoppers to get one. There has been a lot of discussion about this. Funnyface, if you haven't already done so, go to the "new shoppers" section of the forum. Flash and many other wise sages have posted extremely useful information to help new shoppers understand taxes and other issues. Welcome to the forum!