I never liked the "if it affects your life negatively in any way, you are an alcoholic, whether you drink a case of beer a day or just 1." I've known alcoholics who are totally dependent on booze but are successful or even thriving in life.
I believe in the strict sense "alcoholism" is the physical dependence to alcohol where if one were to suddenly stop drinking, tremors, seizures, and other withdrawal symptoms would develop.
More generally, I believe alcoholism is a physical OR MENTAL dependence to alcohol in which one does not have the ability to control or curtail his or her pattern of drinking.
I am an alcoholic myself, although I consider myself slightly reformed in that I only drink on the weekends, and at home. But I find myself unable to NOT drink on the weekends. I have a mental addiction still and am unable to control the pattern of my drinking. I am not physically addicted and my life is going reasonably well, but I am still an alcoholic.