What kind of "fighter"?
Who is the best fighter in the world?
This is a good list of the top MMA fighters that ever lived. Doesn't include Boxers.
I consider your question through boxing. As your question is not exclusive.
Mike Tyson (We also lost a legend very nearly)
Ronda Rousey
Fictional characters: Rocky!
Dear Katherine Smith,
If you include someone we just lost but still contemporary, then you would have to consider Muhammad Ali...
(I saw he is second on the list RC found.)