One question that's often on advertisers' must-ask list is why their site does not begin to appear in Google's free search results once they have started advertising with AdWords. By way of illustration, here's a recent question (slightly edited, and excerpted from a longer post) from the AdWords Help group:
We are the only "widget" company in Santa Barbara County. When someone does a search using for example "widgets Santa Barbara" our sponsored link shows up at the top of the list. This is how it should be and it means that AdWords is working properly. However, why is it that our site does not show up in the free results?
It's important to know that Google's advertising programs are entirely independent of the unpaid search results. So being an AdWords advertiser (or AdSense publisher) doesn't affect the inclusion or ranking of your site in the Google search index. Put another way, being an advertiser will neither help nor harm one's inclusion or ranking.
That said, an excellent place to get answers to your search-related questions is the Webmaster Help Center -- where you'll find links to lots of information on topics such as webmaster guidelines and your site in the Google index.
Also, don't forget to take another look at recent Inside AdWords posts regarding Google Sitemaps, another useful tool that may assist you in getting your site listed.
Update: changed Help Center links
