In chronological order, they are:
- The Dark Elf Trilogy (Homeland, Sojourn, Exile)
- The Icewind Dale Trilogy (The Crystal Shard, Streams of Silver, The Halfling's Gem)
- Dark Mirror, a short story in the Realms of Valor anthology.
- The Legacy of the Drow series (The Legacy, Starless Night, Siege of Darkness, Passage to Dawn)
- The Paths of Darkness series (The Silent Blade, The Spine of the World, Servant of the Shard, Sea of Swords)
- The Hunter's Blade trilogy (The Thousand Orcs, The Lone Drow, The Two Swords)
- The Transitions trilogy (The Orc King, The Pirate King, The Ghost King)
- The Neverwinter series (Gauntlgrym, Neverwinter, Charon's Claw, The Last Threshold)
- The Sundering (The Companions, Book 1)
- The Companions Codex series (Night of the Hunter). Ongoing.
My actual recommendation is to read them in publication order (swap the first two series) as Drizzt changes significantly between the first series and later ones. To my mind he is more an atypical drow rather than the pure force for good he ends up being in later series.
And if you want my really harsh recommendation, speaking as someone who read up to the Hunter's Blade trilogy, read the Icewind Dale Trilogy and stop there. :)