Concept: Ownership

Just a quick one to start this sucker off.

One of the concepts that games often have trouble with is properly making something feel like it belongs to the player. FPS games are probably the worst for this, with practically all the equipment feeling like it's essentially on loan to the protagonist. RPGs with equipment also often fall prey to this, as worse equipment is thrown aside as soon as something superior is found. Recently, some games have tried to subvert this by allowing the player to upgrade their equipment as an incentive to keep it around, an example of this being GSC's S.T.A.L.K.E.R. series, at least in its later incarnations. S.T.A.L.K.E.R. allowed the player, with the help of a mechanic, to upgrade the statistics of their weapon, such as fire rate, or to give the weapon more obvious upgrades, like a thermal scope. This was made a viable option because of the semi-RPG nature of the game limiting the weapon choices of the player. Even so, a fully upgraded weapon could quite often simply be inferior to the next weapon in its respective class, and so the upgrades simply slowed the process of obsessive upgrading. Many modern RPGs have a crafting system, for instance, that allows the player to custom-build their own weapon, but when it takes an unreasonable amount of time to make a superior weapon, as it often does, what's the point? The recent re-release of Tactics Ogre, for instance, requires the player to grapple with a chance-based, arbitrarily unfair crafting system to create superior equipment.
That said, there's a lot of little things that a game can do to make a set of equipment feel like it truly belongs to the player. In Mount & Blade, for instance, the game's medieval setting and devotion to plausibility, if not strict realism, means that various weapons in the same class will have different merits, such as speed or length. The mediocre shooter Army of Two's main strength was the robust weapon customization system that allowed for a fairly unique weapon, particularly in the sequel.
So why is it so important for a weapon to feel like it belongs to the player? It's a way of creating emotional attachment. Odd as it may seem, equipment is one of the player's main ways of interacting with the world, particularly in combat-based genres such as shooters. If a weapon fails to become something that the player is attached to, it's just a verb, or a way to interact with the game world. If it's something the player becomes familiar with as an object, the feeling of interactivity is deepened; the weapon becomes something to use, rather than an action in and of itself, which creates a greater unconscious connection to the game world.

Right, more to come. Feel free to put thoughts, comments, criticisms in the comment pool, that's what it's there for.