I think The Social Network is his best film. It explores the connection between humans (and lack thereof) in a nuanced and powerful way. I think Jesse Eisenberg's performance is spot on, and Fincher's direction is pretty much perfect, both when it comes to atmosphere, pace, structure and editing. The soundtrack is great too.
I also really love Zodiac and Gone Girl.
I could never really appreciate the extreme self-indulgence of Fight Club, the movie isn't nearly as smart or deep as it presents itself as. The music video style editing doesn't help either. It is still a solid film, with some fun ideas and good performances. But it's just that, solid.
I have yet to see Panic Room, Mank and The Game, but the rest of his films I would rank like this:
1. The Social Network
3. Gone Girl
5. The Girl with the Dragon Tatoo
6. Fight Club
7. Alien 3
8. The Curious Case of Benjamin Button