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.