If you know me well, you probably know that I am a fan of the Halo series. I have logged in over 900 matches total in Halo 2 and Halo 3 combined and have spent some time messing around with the Forge editor (most of the time, unsuccessfully). But when asked my favorite Halo game, I can't really give a good answer. I like all three games, but I like them in different ways.
In terms of the overall package I like Halo 3 the most. Even though the campaign had some difficulty curve issues and Forge could use less restrictions and more options, it feels to me like the most feature-rich version with multiplayer maps that were fun to play on, some great user-friendly features (Forge and Custom games, anyone?), and a campaign with some memorable levels and moments.
But in terms of an artistic approach, I like Halo 1 and 2 better. With Halo 1, it's the music; from the melancholy menu theme to the memorable background music. Halo 2's music was less memorable, but it was still superb. Halo 3 still had the same great menu theme, but its music seemed to be lacking something. I don't know why, it just... did. The music was still good, but I greatly favor the sound of the first two games.
In terms of graphics, I actually like Halo 2 the best, particularly along the lines of the multiplayer maps. To me they had an ambient look to them that the maps in Halo 3 didn't have. Because of this I had more fun playing on them. With Halo 2, almost every map was a masterpiece. In Halo 3, only a few maps so far are memorable (the remake of Zanzibar and High Ground come to mind), and though the maps were still fun to play on, I would have preferred a remake of the Halo 2 maps than the new Halo 3 maps. I found all three of the new maps memorable when Bungie released them, so that's a good sign for the future.