The question whether Krishna actually existed or not has arisen since the European scholars began to study the Hindu mythology. See the mystical cycle - first the European scholars realize that the Hindu mythology is very powerful and deep; then they try to read & understand the same; at the end, there is a question over Hindu mythology. Why? As far as I understand, it is because to understand the mythology, one needs to come out of the interwoven traditional beliefs - something easier said, yet difficult to do it practically.
The West does not believe in ‘Life after Death,' which as per Hindu mythology is true. There are different perceptions of life and to understand each one of them - we need to see each one as a seperate ‘identity.' Mixing idealogies of one mythology with another raises questions over ones own belief.
I am not here to justify the statement ‘Krishna existed,' nor am I here to criticize the European scholars/the West. All I believe is, that if Krishna did not exist on earth - where from do the lessons of Bhagwat Geeta and Mahabharta arise? Where from the case studies on Krishna in B-schools come from? How did the faith of 1000's of people in Shri Krishna develop?
For me, Krishna is a source of faith, purity, holiness and is an icon of Lord Vishnu.