Halo 2 brought in vehicle hijacking, dual-wielding and the ability to play as Elites online. Halo 2 also made vehicles more powerful, in that someone with a sniper rifle couldn't kill someone inside a tank unless the hatch was busted off. And vehicles exploded meaning you couldn't kill someone inside so easily and steal it.
Halo 3 brought in deployable equipment, ability to tear off turrets and use them in a mobile fashion.
Halo Reach took away dual-wielding, made the equipment a part of your armour that recharged, and changed to equipment to things like: Sprinting, jetpacks, invulnerability (that would destroy a vehicle trying to run you over if timed correctly) invisibility and so forth.
Most of the other differences come down to the weapons used in the games, for while a few were staples throughout the series (pretty much only the sniper rifle, rocket launcher and the covenant plasma pistol, needler and plasma rifle) most of the others changed, and even the ones that stayed throughout changed a bit. Everything from replacing an assault rifle with an SMG, taking the battle rifle and making it the semi-auto DMR, and altering the homing capabilities of the Plasma Pistol's charged shot. Vehicles changed a bit throughout the games too.