The Halo games brought regenerating health and the two-weapon limit. The latter is traceable to gamepad restrictions and is a little annoying, but undeniably presented a new level of choice to FPS games. The former is strangely divisive, as the people who claim regenerating health is unrealistic seem to fail to notice how unrealistic it is to have magical bandages placed round a map which cure bullet wounds. Both are silly, both are necessary, both lead to different kinds of fun. Regenerating health means every firefight can be treated as a distinct entity where all players are on an even keel aside from their possible weapon loadout. Health packs require more balancing or more nonlinear levels where exploration is encouraged. Both have merits, but personally I prefer the combination of both as per Halo 1 or FarCry 2.
For me, health packs were always made more ridiculous by the fact you couldn't take them with you to use later. Vietcong allowed you to always have 1 health pack to use if you couldn't reach your medic, this was a pretty damn good way of doing things but still, why only one health pack?
Halo games will always be better than the dreaded Modern Military Shooter in my eyes at least.