Medium Shot
Contains a figure from the knees/waist up and is normally used for dialogue scenes, or to show some detail of action. Variations on this include the TWO SHOT (containing two figures from the waist up) and the THREE SHOT (contains 3 figures...). NB. Any more than three figures and the shot tends to become a long shot. Background detail is minimal, probably because location has been established earlier in the scene - the audience already know where they are and now want to focus on dialogue and character interation. Another variation in this category is the OVER-THE-SHOULDER-SHOT, which positions the camera behind one figure, revealing the other figure, and part of the first figure's back, head and shoulder.
Close-Up
This shows very little background, and concentrates on either a face, or a specific detail of mise en scène. Everything else is just a blur in the background. This shot magnifies the object (think of how big it looks on a cinema screen) and shows the importance of things, be it words written on paper, or the expression on someone's face. The close-up takes us into the mind of a character. In reality, we only let people that we really trust get THAT close to our face - mothers, children and lovers, usually - so a close up of a face is a very intimate shot. A film-maker may use this to make us feel extra comfortable or extremely uncomfortable about a character, and usually uses a zoom lens in order to get the required framing.
Extreme Close-Up
As its name suggests, an extreme version of the close up, generally magnifying beyond what the human eye would experience in reality. An extreme close-up of a face, for instance, would show only the mouth or eyes, with no background detail whatsoever. This is a very artificial shot, and can be used for dramatic effect. The tight focus required means that extra care must be taken when setting up and lighting the shot - the slightest camera shake or error in focal length is very noticeable.
The Bird's-Eye view
This shows a scene from directly overhead, a very unnatural and strange angle. Familiar objects viewed from this angle might seem totally unrecognisable at first (umbrellas in a crowd, dancers' legs). This shot does, however, put the audience in a godlike position, looking down on the action. People can be made to look insignificant, ant-like, part of a wider scheme of things. Hitchcock (and his admirers, like Brian de Palma) is fond of this style of shot.
High Angle
Not so extreme as a bird's eye view. The camera is elevated above the action using a crane to give a general overview. High angles make the object photographed seem smaller, and less significant (or scary). The object or character often gets swallowed up by their setting - they become part of a wider picture
Low Angle
These increase height (useful for short actors like Tom Cruise or James McAvoy) and give a sense of speeded motion. Low angles help give a sense of confusion to a viewer, of powerlessness within the action of a scene. The background of a low angle shot will tend to be just sky or ceiling, the lack of detail about the setting adding to the disorientation of the viewer. The added height of the object may make it inspire fear and insecurity in the viewer, who is psychologically dominated by the figure on the screen.
Crane Shots
Basically, dolly-shots-in-the-air. A crane (or jib), is a large, heavy piece of equipment, but is a useful way of moving a camera - it can move up, down, left, right, swooping in on action or moving diagonally out of it. The camera operator and camera are counter-balanced by a heavy weight, and trust their safety to a skilled crane/jib operator.
The Aerial Shot
An exciting variation of a crane shot, usually taken from a helicopter. This is often used at the beginning of a film, in order to establish setting and movement. A helicopter is like a particularly flexible sort of crane - it can go anywhere, keep up with anything, move in and out of a scene, and convey real drama and exhilaration — so long as you don't need to get too close to your actors or use location sound with the shots.