Well, I've been thinking about this for a while, so I thought I'd put in a list. These are mostly for the purpose of immersion, but could be used strategically. With modern processors, these should be feasible.
The character's hands. I've got problems with not seeing the other hand, or even the one holding the gun. Games that do this: Prime series when there is an explosion close by, Crysis when grabbing someone, Halo when you've got the sword.
The rest of the character's body. This annoys me too. If I back into a corner and look all the way down, I should not be able to see the corner behind me. It should be obscured by the rest of the character's body. Games that do this: Halo 3 shows MC's legs below him when you're jumping and looking down. There was another game (I forget which, but it was probably either FEAR or a sequel? I don't keep up with the games; just saw a trailer) where the camera shifts cinematically when you kick something out of the way and you see yourself actually make contact with the object. Crysis probably does this as well; I haven't seen too much of it.
More realistic reload. I mean, come on. You can't reload a pistol as fast as this guy on the battlefield. Also, make it timed like Gears of War, and if you screw up you drop the clip or jam the gun. This is mainly an immersion thing, like the previous two.
More realistic gun and ammo pickups. If a gun is on the floor, make a duck to pick it up instead of just automatically grabbing it. If it's on an elevated surface, show the arm grabbing it and throwing it over shoulder/shoving it in holster. Make it so you can keep firing while this is happening, so it's not so inconvenient.
Drop guns on impact. Another immersion but potentially strategic detail would be to drop your gun when a grenade or explosion gets too close, or when you get hit by a vehicle. If a hit takes you down to extremely low health, there should be some effect. If not during explosions, how about in deep water? Since we don't see water very deep in games, it's not very fair to demand this, but i would say drop the assault rifle when you hit the waves. Automatically you would have to swim back to shore then pull out whatever you've got as a secondary. Also, it would probably be jammed. I don't know of any games with this type of thing.
Ledge grabs. This is more of a personal preference. I liked how it worked in Prime 3, but how about every ledge? You could drop below on a ledge and wait for a foe, then pop up and knock them over. Or at least you wouldn't accidentally fall off a cliff because you couldn't see your feet.
Grenade kick. This was in MoH games for a while (and still is?). Basically, if a nade comes in near you you can kick it back. Very useful and realistic.
Weaker pistolwhips. It's just ridiculous how one hit from the butt of a pistol is better than five bullets from it.
Gun wrestling. C'mon, it's fun in the movies. When you get close enough to a guy, you should be able to grab his gun and wrestle it from him, then use it to blast him close range. More effective and unique than a pistolwhip, but leaves you vulnerable.
Sprint and trip. How about the ability to run very fast, but if you hit a wall or run into a crate you trip? This was my favorite innovation of Assassin's Creed.







