We are the only "widget" company in our county. When someone does a search using, for example, "widgets my county" our sponsored link shows up at the top of the list, which is how it should be...How can I get our site to show up in the free search results too? - Not there
We're happy to shed some light on this. To start, here's a brief glossary:
Sponsored links: the paid AdWords ads at the top and/or on the right hand side of a search results page
Search results: the unpaid search results on the left hand side of the page
The most important thing to know is that there is no connection of any sort between the unpaid search results and the paid sponsored links -- so being an AdWords advertiser will neither help nor harm one's ranking within the search results.
This leaves the important question of how to get your site to appear in the search results, since being an advertiser is not a factor in being included. Well, we'd be pleased to help you on your way. You'll find some very useful information on this topic on the Google Information for Webmasters page, including answers to such frequently asked questions as "How Do I Get My Site Listed on Google?".
Also, be sure to refer to our past posts about Google Sitemaps, which allows webmasters to give Google information about their sites so that we may index them effectively.