Prepare for lots of monotonous reading...
I probably should have clarified whether this thread is about your FAVORITE Halo game, or what is the BEST made Halo game. Either one works, I guess. In terms of multiplayer, I definitely think Halo 4 is the best (kidding). Halo 2's and Halo 3's mulitplayer are both so good, I can't really decide. Reach's is pretty damn good, too.
I think it's hard for me not to select Halo 3 as the best Halo game since it was my first Halo game, and the amount of nostalgia I have for it is monumental. Obviously, my opinion is extremely biased because of this. I bet that most (or at least a decent proportion) of people's favorite Halo game is also their first Halo game that they played.
But honestly, Halo 2 added so much to the Halo franchise without really changing the Halo formula. Just think of all the changes implemented from Halo CE to Halo 2. It expanded the vehicle and weapon sets (dual wielding, too), added new enemy types, pioneered online multiplayer on consoles over Xbox Live. it expanded the lore and the Halo Universe by adding new settings and characters, and so much more. But despite all of these changes, it was still Halo at its core, and it improved on Halo CE's mechanics without breaking any of CE's mechanics. Halo 2 is a near-perfect sequel. Does that make it the best Halo game? Maybe.
Also, ODST is really underrated. But I've rambled on enough. Ending post in 3, 2, 1...