Single player: Half-life.
Multi player: Unreal tournament.

Regenerating health(used in 95% of modern games in every genre)

Console online mmultiplayer 

two gun system

seperate Melee button

auto aim

modern first person control scheme

console user generated content, theater system

the survival of the Xbox brand

those are just the things it heavily influenced or created, halo is also pretty much responsible for the success of console shooters, halo wasn't the first console FPS but it was the first that could rival pc shooters. For being responsible for the rise of FPS halo is indirectly responsible for the rise of western game development(Japanese dominated before 2001 because westerners are best and making shooters and those weren't popular) it also popularized wide open environments over small corridors and it revolutionized shooter storytelling. Halo also turned gaming into a blockbuster industry, halo 3 was the first game to become the largest entertainment launch of all time, games didn't have huge hyped up launches that could beat movies before halo, halo did the same thing to games that Star Wars did to movies. There are many other ways I could talk about halos influence but I think that's enough for now. There are very few game series I can think of that have had that much influence on gaming.

Call of Duty and Medal of Honor.

Consoles had great online multiplayer long before Halo, although it did introduce match-making (unless I'm mistaken). I'm pretty sure that you're wrong about seperate (sic) Melee button, auto aiming and a modern first person control scheme. Also, I can not stand the two weapon limit. I like imagining Resistance 2 if it wasn't marred by that.

Metroid Prime

Console online multiplayer was garbage and no one use it before halo 2. And I don't see any examples for games that did those before halo? I also said popularized not jut invented(although I still think halo invented those things until i see evidence to he contrary) and it doesn't matter if you can't stand the system, action games have heavily benefited from it. Because you mentioned resistance 2 I take it you're a ps3 fan so it is expected that you would deny halos influence.

P.S. the developer of splinter cell blacklist(A GAME DEVELOPER) credited halo for auto aim so I'm pretty sure you're wrong.

Call of Duty, for me. Simply because it took up more of my time than any other FPS.

where is team fortress 2

Resistance franchise.. since i love Si-Fi FPS the most and the story was outstanding. not to mention the diversity for its weapons in R1 & R3 and the Co-op mode in R2. the controles overall suits me best.