The best biography I have read about Napoleon would be by Andrew Roberts called Napoleon: A Life. It does a good job of balancing the praise that Napoleon deserves for the good he did and the criticism that Napoleon deserves for his slow slip into egotism. It's relatively new and does a lot to tackle myths and historiography of Napoleon. I highly recommend it.

"Best" is going to be highly subjective, as Napoleon is a highly polarizing figure.

Personally, I am rather fond of Philip Dwyer's two-volume biography Napoleon: The Path to Power and Citizen Emperor. Dwyer is very critical of Napoleon, but does make a persuasive case about the emperor's shortcomings and give the man credit when it is due. Michael Broers's Napoleon: Soldier of Destiny, volume I is a recent biography that incorporates new research from Napoleon's correspondence. If these multi-volume biographies are too daunting, Geoffrey Ellis's Napoleon is part of Longman's Profiles in Power series and intended as an introduction to major historical figures.