Light is pretty much the most important source for photography, without it no photographs would even be visible. Different types can be used to create different effects with various sources. If you click on the pictures you are taken to the website of their owners.
This light is aimed at the subject of the photo in the same direction it is being taken, for example next to the camera. This differs the background colours (more dark) to the subject of the image which the light will shine on and brighten for the photograph, can result in particularly flat effects though.
This is the opposite of front lighting, the source of light whatever it may be is aimed behind the subject so that the background is more bright/illuminated than the subject, particularly good when wanting to create silhouettes of the subject, so for example would not be suitable for a high quality portrait photograph. it can also create a glow around the edges which can be particularly effective.
This lighting comes from a large source or even multiple sources, this is so that instead of resulting in harsh edges and contrasting colours that one single light beam would, it creates more of a soft natural looking effect, e.g the similar effect fog gives to natural scenes, looks more gentle on portrait photographs too but can make some detail quite minute.
This comes from a single light source such as a light bulb, it falls on a particular object with no reflections/different directions in the way. It creates dramatic shadows that are shown in full sharpness making them seem harsher and more contrasted with the lighter colours in the photograph.
Although going by the name, this lighting doesn't need to be set up in a studio, these lights can be strobe lighting, fluorescent or HMI mainly. The light sources can be dimmed/diffused by being reflected off of other surfaces such as umbrellas, soft boxes, so that the effect is still there but less harsh, works particularly well in black and white because of the shadows shades, also for fashion photo shoots.
Very accessable, no artificial sources needed, makes use of the worlds natural lighting which is either sunlight or moonlight. Brilliant for outside and landscape photographs.
This creates a spotlight effect, most useful when say illuminating a certain subject whilst taking a shot in the dark. (photo below taken by me).
Created by laser pens, can be any colour at all and usually used for light paintings (some which I have tried to produce myself), creates a harsh bright line in contrast to darkness (where it works best by far).