Halo 2 really brought the whole "2" thing - you could dual-wield weapons, you played as two separate characters throughout the game, and the game was 2 (divided by four) the total of one game. By that, we mean it was sorta half a game, as the game abruptly ends with Master Chief traveling via bomb through space to battle the Covenant on Earth. Which, ya know, is fine and all, since the big takeaway from Halo 2 was its incredible multiplayer, which is still held up as a highpoint for the series, with more diverse maps, more customization, and the terrifying, nightmare-inducing sound of a sword being activated.
Possibly the greatest co-op game ever, the hallmark of LAN parties, and the cause of untold cases of computer mouses being wrecked from overclicking, Diablo II was definitely the best game ever about murdering Satan (resurrected after your bizarre decision to shove a crystal into your forehead at the end of Diablo Uno). The game was damn near perfect - improving on pretty much everything started by its predecessor, and standing as an impossible goal for its follow-up, That Game We All Played For Like A Week In 2012.
After GTA III's enormous success, Rockstar figured they had to get another one of these money-printing chaos-simulators out ASAP - the only question was how to distinguish it from GTA III's "sorta New York-ish city." The answer - "sorta Miami-ish city." Also: the 80s. Also: motorcycles. Also: Ray Liotta. Also: swimming...haha just kidding, they somehow made a game with 50% more water that was still insta-death. Why didn't the news get all riled up about THAT?
The last proper console entry in the Kingdom Hearts saga came out nearly a decade ago, but proved the series had legs - in spite of some confusing plotting and gameplay, it had better graphics, fighting, and managed to keep Haley Joel Osment employed in spite of Not Being An Adorable 8 Year Old anymore. But, as usual, one of the best parts was getting to explore new Disney worlds, including Mulan, Pirates of the Caribbean, and The Lion King (although no "SEX" dust references). Sadly, we're still waiting on Ridiculously Racist World from Song of the South.
Mario Kart 64 took the basic idea of its predecessor (Mario and his friends and enemies get together to race when not kidnapping/murdering each other) and brought it into glorious mostly-3D (the character models were still pixel-based). Mario Kart 64 became a benchmark for the series, setting the tone for everything to come - from the items, the multiplayer, and the constant misspelling of "cart."