He is an evil Drow that managed to escape his heritage and become a hero despite all the odds stacked against him. He's also a nearly supernaturally good fighter that stands up for the weak and innocent while fighting demons, dragons, and opposing the will of gods. He's also intelligent, introspective and brooding. He's got interesting friends and goes on interesting adventures.
Like most characters in stories, whether you like him or not is kind of a personal choice. I like him. Although, I find he is very often written as a Mary Sue character so I have to roll my eyes whenever Drizzt is written to literally be the best at EVERYTHING on the planet. Too many times during the novels you find that R.A. Salvatore writes that Drow are the best at everything. The best fighters in the world are Drow, the best Wizards in the world are Drow. Drow are the stealthiest of all the races. Drow children are better at sneaking than the best Thieves in the world. But among the Drow, Drizzt is considered the best of the Drow. He was their best fighter, he was the best at sneaking. He doesn't cast spells but(if I remember correctly) he seemed to have the aptitude for it and might have been the best Wizard ever if he had chosen that path.
I think a large amount of the backlash towards him is precisely for that reason. He is written often as a power fantasy. You get to look through his eyes during the novels and you get to experience what it's like to be the best of the best. But after a while, it can seem a little contrived.