Do You Have To Have A Business In Order To Use Google's Adsense Program?

No you do not need to have a business to use adsense.

What you WILL need is either a website or a blog and it has to be approved by adsense first before you can add the ads to your site.

You will have to give them your social security number because since they are paying you they have to report and YOU have to report it. (Of course having to report your adsense income as income will depend on how much income you earn from adsense)

Here is a link to what some people (and I stress - people) are earning using adsense:

Just How Much Money Are People Making Using Adsense?