A lot of people like to say The Two Towers is the best, but all I remember from that film is the battle of Helm's Deep. My ranking goes Return of the King > Fellowship of the Ring > The Two Towers. All three are great, but the best character work and the best action are in The Return of the King, while the Fellowship has the most memorable scenes for me, personally (Since at this point it hadn't turned into an all-out fantasy war film by then and still had loads of joy and terror).
Like I said, all three of them were truly outstanding films and might be the best film trilogy of all time, but that's my ranking.
Then again, I actually DO like The Hobbit trilogy, even if I think it'd have been better if it was a single movie as opposed to a trilogy.
My Console Library:
PS4, PS3, PS2, PS1, WiiU, Wii, GCN, N64 SNES, XBO, 360
3DS, DS, GBA, Vita, PSP, Android
Top 6 this generation:
Bloodborne, Sekiro: Shadows Die Twice, God of War, The Legend of Zelda: Breath of the Wild, Dark Souls III, Red Dead Redemption II, Rock Band 4