I realize that the company will need my social security number to pay me, but I've already found at least one or two companies that allow you to REGISTER to shop with them without giving an SSN in the application. Again, I think there's a good chance I will never wind up doing a shop with many of these companies, and I don't want to give them my SSN upfront.
I have a coworker who is going through a nightmare with identity theft so I'm a little sensitive about distributing my SSN all over the internet.