I was checking my stats and notice over 400 404 errors for a robots.txt file which I do not have. Can it hurt my rankings with the search bots if they are looking for this file and getting a 404 error?
No, but just place a blank file in the root of your website so you dont have to see the errors in your reports.
it most certainly does not hurt your rankings. if it disconcerts you, like the above poster said, you can upload a blank file. or go the brett tabke route
like what search engines? yeah search engines use the robots.txt as like knocking on the door to your site. You not having a robots.txt is like not having a door so the seach engines can go write in