Halo 3 hands down - though I guess the same can't really be said nowadays.
Back during it's release Halo 3 was
the definitive game of the Xbox 360. No single game will ever define a console as strongly as this game did in my opinion.
After it's release, Halo 3 was essentially the Xbox 360 dashboard for a few years. It was always an experience making a custom game lobby and inviting everyone on your friends list, and having them do the same. It was SO easy to fill up a full lobby and play some really obscure gamemode that nobody had played until then - as well as the classics that everyone played just about every day. (Jenga, Duckhunt, I am Legend, etc)
I feel one of the reasons Halo 3 was so IMMENSELY successful was because it was one of the few major games that was released before the implementation of the party system for Xbox Live. Before that implementation, all communication took place in the game lobby, which made the game EXTREMELY sociable, and was half the fun. After the implementation is when I remember the game's activity dying down.
Since you could always stay in a private party with all of your friends, there was never really a reason to talk to anybody else, and so this really weird system of inviting everybody you could and massively expanding your circle of online friends seemed to just die. This is why I think Halo Reach and Halo 4 simply couldn't compare to Halo 3's popularity, and it's very sad to think about because in my mind it's that one feature which singlehandedly killed Xbox Live for me.
But enough rambling and ranting and whining.
My current favorite Xbox game is Rainbow Six Siege. Not because I play it on Xbox but because I play it an absolute TON on PC and it happens to be on Xbox.
I like it a lot.