Google.com tends to be my first stop when I'm considering working with a new person.  A new website called pipl takes the idea a step further.  Unlike traditional crawlers like Yahoo and Google, the pipl search engines can access various public databases - from e-commerce to social networking to government records - and therefore generates a lot more hits. 

Look yourself up - you might find that there is more info on you out there on the web than you thought.  One drawback: search for a generic name (like, say, Chris Smith) and you'll get a whole boatload of info on all the other Chris Smith's out there.   [19 June] Ironic postscript:  As of today this page that you're reading right now comes up on page 1 of a Google search for "Chris Smith"

When you're screening tenants you'll still need to pay for a real background check, but I think this site might be useful for the quick preliminary screens I used to do on Google.