This article aims to address the question: how does your digital camera's sensor size influence different types of photography? Much confusion often arises on this topic because there are both so many different size options, and so many trade-offs relating to depth of field, image noise, diffraction, cost and size/weight.
Sensor sizes currently have many possibilities, depending on their use, price point and desired portability. The relative size for many of these is shown below:
Canon's 1Ds/1DsMkII/5D and the Kodak DCS 14n are the most common full frame sensors. Canon cameras such as the 300D/350D/10D/20D all have a 1.6X crop factor, the 1.3X crop factor is used in Canon's 1D series cameras.
Camera phones and other compact cameras use sensor sizes in the range of ~1/4" to 2/3". Olympus, Fuji and Kodak all teamed up to create a standard 4/3 system, which has a 2X crop factor compared to 35 mm film. Medium format and larger sensors exist, however these are far less common and currently prohibitively expensive. These will thus not be addressed here specifically, but the same principles still apply.
The crop factor describes the sensor's width ratio to a full-frame 35 mm sensor. It is called this because when using a 35 mm lens, such a sensor effectively crops out this much of the image at its exterior (due to its limited size).
One might initially think that throwing away image information is never ideal, however it does have its advantages. Nearly all lenses are sharpest at their centers, while quality degrades progressively toward to the edges. This means that a cropped sensor effectively discards the lowest quality portions of the image, which is quite useful when using low quality lenses (as these typically have the worst edge quality).
On the other hand, this also means that one is carrying a much larger lens than is necessary-- a factor particularly relevant to those carrying their camera for extended periods of time (see section below). Ideally, one would use nearly all image light transmitted from the lens, and this lens would be of high enough quality that its change in sharpness would be negligible towards its edges.
Additionally, the optical performance of wide angle lenses is rarely as good as longer focal lengths. Since a cropped sensor is forced to use a wider angle lens to produce the same angle of view as a larger sensor, this can degrade quality. Smaller sensors also enlarge the center region of the lens more, so its resolution limit is likely to be more apparent for lower quality lenses.
Similarly, the focal length multiplier relates the focal length of a lens used on a smaller format to a 35 mm lens producing an equivalent angle of view, and is equal to the crop factor. This means that a 50 mm lens used on a sensor with a 1.6X crop factor would produce the same field of view as a 1.6 x 50 = 80 mm lens on a 35 mm full frame sensor.
Be warned that both of these terms can be somewhat misleading. The lens focal length does not change just because a lens is used on a different sized sensor-- just its angle of view. A 50 mm lens is always a 50 mm lens, regardless of the sensor type. At the same time, "crop factor" may not be appropriate to describe very small sensors because the image is not necessarily cropped out (when using lenses designed for that sensor).