Allen Iverson was the most dominant ball handler of all time. He redefined the game with his dribbling ability. He was probably the first player to exclusively use ball handling as a way to get an open shot. And you rarely if ever saw a player prevent AI from getting a clean shot off. Unlike the great ball handlers before AI, he would use his dribbling to score points instead of setting up teammates. This was a semi new skill because it's harder to get the ball into your shooting pocket for a clean look off of an advanced dribble then it is to simple dish off a nice pass.
What made AI's ball handling so special was his pull up ability. He could get the ball from a double behind the back crossover into his shooting pocket for a clean shot, better, a quicker then anybody you'll ever see. He literally dominated the league with his dribbling and speed.
Chris Paul and Steve Nash are 2 and 3.