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The quickest and easiest way to start making money without a website is with www.twiter.com. If you do not have a Twitter account, you can sign up and start promoting your affiliate programs and earn money right away. This can also be done with Myspace, FaceBook and many of the other social networking sites.
Another great way to start making money without a website is to find (Google search) forums and message boards that are related to the products and services you are promoting. By joining the group and posting useful information to the board, you will be able to sneak in a few product promotions.
You can also do a search for websites that are related to your product or service and see if they have a guestbook. Make a nice entry in the guestbook and in the place where they ask for your website, enter your affiliate link.
You can also use your email address to promote your products or services. You may not want to just exploit your friends and straight out try to sell them stuff, but you can create a signature or tag line that will be at the end of the email so you will not be seen as a "hard salesman", your recipients can click the links if they want to. You can even disguise the link to look like it was put there by the email provider..