What is cinematography? Not many people talk about it in video games, but cinematography is the art of making motion pictures. Good cinematography is able to present not only what is necessary but also what is necessary with meaning, purpose, and direction. Like user interfaces, good cinematography can be so easily missed and generally is.
In games where only the player controls the camera, the player is the one to decide what is on-screen. As a result, their attention must be directed by the environment. One technique is to utilize anything that requires immediate attention, like enemies. Another technique is to light things that are important or of interest, as seen with the Half-life series. Most cameras during gameplay are like this, functional but unimpressive. League of Legends, Half-life, Assassin's Creed, the list goes on. The cameras do what they need to do but not much more than that; though by the nature of the games' genres, the cameras will inevitably end up like this (see FPS and multiplayer games).
Looking on the flipside where the player cannot control the camera, the developers must manage it. In 2D, the camera can be as simple as following the same motions as the player. But if we dig deeper, we find that even in 2D the camera can be very nuanced. Take for instance the Super Mario series, the earliest camera is pretty straightforward: if the player moves right past a certain threshold, the camera moves right. This is taken one step further in later incarnations by incorporating the player's speed into the mix to give a sense of momentum. (I definitely suggest checking out the recommended watch and source of this entry shown at the bottom if this interests you.)
The most impressive cameras are those where the games are able to manipulate them to give the shots meaning, purpose, and direction. Take Shadow of the Colossus for instance. When the player rides horseback, the game will often maneuver the camera to zoom out and pan to encompass the enormity of the world and how small the player is in respect to it. And then when the player wants to look somewhere else, the camera is still responsive enough to allow the player to do so. As an example of a game in which the player has no real control over the camera, there is Silent Hill 2. The weird camera angles and shots accentuate the unsettling nature of its world, never allowing the player to relax from cut to cut.
Cinematography adds so much depth and beauty to video games because we as humans perceive so much through our eyes. To be able to take full advantage of it gives visual media vitality in the same way that grammar does for writing, color does for art, and inflections do for speaking. These important things that are often times unnoticed by us should always have a chance to be recognized and appreciated. What are some of your favorites?
Recommended watch and source: "Scroll Back: The Theory and Practice of Cameras in Side-Scrollers" by Itay Keren from a GDC http://www.gdcvault.com/play/1022243/Scroll-Back-The-Theory-and