I noticed something interesting looking at my AdWords statistics today. On a few keywords where my site is the #1 search result in Google I get a very high CTR and pay a very low CPC for my ads running on that keyword.
For awhile I thought I should shut off these ads. Now I am not so sure. I was already the #1 search result but somehow surfers are clicking the ad. Would they have clicked an ad anyway? In other words, would they be visitors I would not have received without my ad?
If I were paying more for these clicks I'd probably shut them off, but I am getting them for about half of what it costs me.
I'd leave them running, especially if you are getting the cheap clicks. You will build up a history that newcomers will have a hard time competing with for your spot. Also, you may be #1 for the organic search NOW but your only one algo tweak away from #345369!
Also, being number 1 on both organic and sponsored may reinforce to users that your site is the authority for that particular keyword phrase. This could result in increased CTR (hopefully on your organic listing).