To evaluate and compare the relative popularity of fighters from different historical eras, I used four separate and more or less equal criteria:
1. Stature and fame within the sports world and popular culture of their own era;
2. Lasting visibility within modern popular culture;
3. Actual historical importance as a fighter;
4. Genuine affection from the public.
I have tried my best to make this an objective list. This is not a list of my 20 favorite fighters.
However, I am a 41-year-old American fan and that shows. I've selected fighters from the late 1800s through the present, but fighters from the 1970s, '80s and '90s are heavily represented. There is also a clear bias towards North American fighters, with popularity largely defined by visibility within the United States media.
For example, the Klitschko brothers' fights in Germany have the atmosphere of rock concerts and the two are major celebrities both there and in their native Ukraine. A European fan could fairly object that the brothers are as popular as many of the fighters on my list.
Heavyweights dominate here, which should hardly come as a surprise. For many decades of the 20th century, boxing was among the most popular of professional sports and the heavyweight champion, by definition, was one of the most popular heroes of the day.