Visit Googlefone, and you can enter a name of a person or business, plus some location data, and you'll be shown any matching publicly-listed numbers that Google knows about.
Tara Calishain has a long-standing interface that works similarly. It will only check business listings, but the drop down box with US states is nice.
Courtesy of Tara, another write-up from her explains how you can also use some power commands or search syntaxes to tap into the phonebook. Do a query like:
phonebook: edwards california
That will show all business or residential listings that match. Use bphonebook to just check for business listings and rphonebook to just check for residential listings.
He also notes that Yahoo provides a way to check its own phone service, Yahoo People Search. Unlike Google, Yahoo conveniently provides its own direct interface right on its site, rather than leaving it for others to create.
The idea that people might find your phone number freak you out? Get an unlisted number, as these services pull from public sources. But you can use special forms at Yahoo and Google to get out of their listings, if you're currently showing.