Drizzt Do'Urdan, if you don't know him, is a character from R.A. Salvatore's fiction set in the Forgotten Realms. He has become the most popular character from the Forgotten Realms campaign setting, and anyone who has scanned the young adult fantasy section of their local library has probably seen him on a cover: a dark-skinned, white-haired elf with two swords.
He is a dark elf, also called Drow (rhymes with cow). Drow are an evil, dark-skinned race of elves that have been shunned by their forest-dwelling brothers and live underground worshiping the spider goddess Lloth in a matriarchal society. Drow are creepy and evil, but organized. Kind of like the Sith, but with pointy ears and more complicated names.
Drizzt is unique, because he rejected the evilness of the Drow, leaving his home city of Menzoberrenzan (I did say they had complicated names) and venturing to the surface. Once there, he was met with rejection, hatred, and racism against him, because of the wrongs of his people. Drizzt is a Ranger (by class/job) and does his best to right wrongs and help people, despite their hatred. That underdog element, and the sense of personal sacrifice, is one of the driving themes that makes Drizzt an enduring character in the eyes of Salvatore's readers.
That same element, though, is responsible for what I think of as "The Drizzt Problem". Simply put, everyone wants to be like Drizzt. Wizards of the Coast (the gaming giant that bought Dungeons and Dragons back in the 90s) knows this, so they built Rangers in a way to make it easy to use dual-wielded swords effectively. As such, many players run characters, ironically in order to be unique, who are effectively Drizzt.
There is no wrong way to play Dungeons and Dragons. In large part, the game is designed to let players be whoever they want to be, and if that's Drizzt, so be it. That said, it can be nerve-wracking to sit down at a table and find 2 players in the same party, who are both playing Drow, who are both of the Chaotic Good alignment. On the one hand, these players have every right to their character's back story as anyone else, but on the other, everyone at the table already knows the contrived drama they expect the DM to prepare for their character. It looms like an ominous black spider queen, ready to talk about herself.
I confess, I have never been in a party with an evil Drow, though I have met about a dozen Drow players in the last year. It's almost enough to make me wonder if there actually are any evil Drow. Maybe Lloth is all about happiness and flowers, and just has a terribly PR group. This oversaturation isn't the end of the world, by any means; I do believe that it is a problem that needs to be addressed though.
Part of creating a character in Dungeons and Dragons involves choosing a concept that you will enjoy playing, that you identify with, and that is engaging for the players around you. While it can be a lot of fun to run a character based off of a book, and while it is very easy to do that, I don't think it's the best option.
I have no right to tell you how to build your characters or run your games, but for the sake of the party around you, try to be original. There is nothing unique and rebellious about playing a character somebody else dreamed up and popularized, even if you change their name. Drizzt can still be fun despite that, but recognize that your character isn't as original as you might hope.
If you do run a good-aligned Drow, great. Just don't expect the party to be very enthusiastic when they see yet another rebel dark elf, attempting to redeem himself for the sins of his people by defending the world that hates him.
To everyone else, try not to be too hard on the Drow player. Just let him do his thing, and to be happy with it. Dungeons and Dragons is about having fun, not harping on the player who wants to relive a series he loves.