Game mechanics that make sense:
A character should be able to jump, climb over objects without a fucking prompt (UNCHARTED, GTAIV), climb on top of objects (UNCHARTED, GTAIV), drop down and hang from ledge (UNCHARTED), be able to fire a one-handed weapon while hanging from ledge while using the ledge as cover (UNCHARTED), and use objects as cover without having a fucking prompt show up all the time (UNCHARTED/GTAIV).
L3 should be used to switch shoulder view while aiming in a third-person shooter.
Melee during a gunfight should take 3-5 moves at most and should be over quickly as not to kill the game's pacing (UNCHARTED).
In a third person shooter, the character's movement should be controlled like a platformer, but the camera CAN be controlled by the player and the aiming reticle should be anchored to the direction of the camera and not the direction the character is facing (UNCHARTED and GTAIV)
There should be as few invisible walls as possible, if the player isn't allowed to go across a certain barrier, erect a physical barrier there (hurhurhur I said erect).
Jump should be executed via a jump button. Not an action button. Jumping should ALWAYS be manual and NOT simply context-driven, press the jump button to make the character jump.
More collision maps give the game more freedom and increases the actual playable area within a level (SOTC, Soul Reaver, Okami), think vertical.
Camera should be controlled with the right stick (up, down, rotate).
A headshot should always be a one-shot kill (unless the bullet hits a protective helmet, in which case the helmet should come off).
Defeating a boss should grant one an ability that enables the player both as a means to open up a new area AND/OR as a new offensive capability (Soul Reaver, OKAMI, ZELDA).
Skills/moveset should be utilitarian and purpose-driven, a skill/move is NOT just an animation with damage attached, it should do SOMETHING (push an enemy back, break a block, hit with a wide damage radius as opposed to a quicker strike with a narrow AOE, launcher, grapple, dash forward, dash backward), 10 very useful moves that the player will be using all the time are always better than having a 100 strings where 99 of them are never used.
A weapon should come with unique ability, speed, moves, element affinity, and all of which should mean something unique than just being a different skin for the same fucking weapon but just with more fucking damage or a slightly different attack animations where there is no practical difference. Gauntlet breaks wall, claw climbs wall, fire sword burns vines blocking path, lighting staff powers device.
Having one weapon in each class that can be upgraded and built upon to be made more powerful throughout the entire game instead of having 100 weapon of the same class having the same fucking animation set.
Meaningful weapons/items instead of "mad loot", have instead energy or essence from dead enemies that power up or keep fueling various abilities in kind of a "sustaining that chain reaction" way.
Flying in game is overrated, large leaps such as launching a manual grapple beam that pulls the player to the target via a super-jump is much more thrilling.
A large boss is only a large boss when that physicality matters more than just the player hitting at the boss's feet. The more manually interactive the boss is (meaning the ability to manually climb and walk on the boss), the bigger the boss becomes even when the boss might not be taking up more space.
QTEs are stupid and lame, they're the worst kind of cutscenes since they actually INTERRUPT GAMEPLAY while regular cutscenes merely allow the game to transition to story-telling upon finishing one level and entering the next, manual control is always better than a QTE, because basically a QTE can indicate that you want to do something but you haven't figured out how to design it properly so you're scotch-taping some cutscenes to a few button-inputs.