When it first came out as an XBox exclusive, it did a lot of things different. First, it already was boosted by the popularity of Bungie, who made tons of other great FPSs like Marathon, and by the marketing of the Xbox. Second, it was extremely original and a new breath in the world of sci-fi and games. Third, it was the first viable FPS with multiplayer on the console--just about every FPS back then was designed for the PC and the consoles were shunned for having nothing on par with PC exclusives, then Halo and its famous multiplayer came along and showed how great splitscreen looks on the next generation. (Yes, Goldeneye and Perfect Dark existed, but they control like a bunch of ass, and Halo again had better marketing).
Halo 2 had the BEST graphics of Xbox, and it took what made Halo: CE great and expanded on it. I think of all games, Halo 2 was the game that made the biggest impact to everyone about the series.
After Halo moved to the 360, there was some things to it that made it stay alive. One is the deepness of the lore and the dedication to the campaign -- obviously underrated and forgotten, since people call the campaigns short and never pay attention to the world Bungie created.
But honestly, it worked because of the splitscreen and multiplayer. It isn't often you have a game with very solid maps and very solid vehicles with very solid combat and very niche-y and solid weapons. It isn't often anymore that you have a sort-of fast paced FPS that doesn't use ironsights and everyone has the same abilities as everyone else. Because Halo places weapons on the map and you spawn with junk (or everything is rocket launchers, another fun thing about Halo), everyone had the same possibilities of going huge and you couldn't say 'fucking superjump perk pro noobs', it was based on skill.
Then Reach ruined what I stated above by making everyone function different. Armorlock or sprint or jetpacks or whatever. I hear Halo 4 now has the Call of Duty class system with perks, and man, that just isn't a Halo game. (Reach still is really fun though.)
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I haven't bought a Halo game since 2, (I've only got Reach because it was a free download with my 360), but I've beaten all of the campaigns except ODST and Halo 4. It's got solid gameplay and its mostly stayed solid, and they never fixed what ain't broke until Reach.
And it works as a supplement for Timesplitters.