There are many types of photographic lenses, the most common categories of which are outlined below. (For a more technical treatment of the subject you may wish to refer to Optics.)

Normal

A so-called 'normal' lens bends light roughly the same way our eyes do, thus providing an image with the proper proportions. It has a focal length close to the diagonal measurement of the image frame. That is, with a standard 35mm format full frame camera, the image on the film or digital image sensor measures 24x36mm. The diagonal measures 43mm (sqrt(36²+24²)). The closest lens most manufacturers produce is the 50mm lens. Cameras with formats other than 35mm have 'normal' lenses with different focal lengths — longer for larger formats, and shorter for smaller formats.

35mm - 50mm (eg. Nikon Nikkor 50mm f/1.4, Canon EF 50mm f/1.4, Pentax smc P-FA 50mm f/1.4, Minolta AF 50mm f/1.4, et al)

645 - 75mm (eg. Pentax smcp-FA 645 75mm F2.8, et al)

6x7 - 105mm (eg. Pentax smcp 67 105mm F2.4, et al)

APS-C - 30mm (eg. Sigma 30mm f/1.4)

You can compare lens focal lengths across various film formats using this external chart.

Wide-angle

Wide-angle lenses have a larger field of view than normal lenses. In other words, they capture more of the scene in front of the camera by capturing more of the periphery. However, as the size of the film or sensor in the camera is still the same, the wider scene appears on the film or sensor as being slightly distorted: the bigger scene is "squeezed" onto the same area of film or sensor, so the typical effect is that each object is smaller (and therefore looks farther away) because the image now "includes" more objects. With each object smaller, the typical effect is that objects seem farther away. What you see in the passenger side wing mirrors in cars is the same. Those mirrors give a wide-angle effect and allows you to see more of the scene behind the car by making each object smaller, hence the common warning printed there: "Objects in mirror are closer than they appear."

There are various wide-angle lenses, measured by the focal length. The "normal" lens for a 35mm camera is about 50mm focal length, and a wide angle lens has a shorter focal length, such as 35mm or 28mm. The shorter the focal length, the greater the perspective distortion. At the extreme end, there are wide-angle lenses with a focal length of 10mm or so using a "fish eye" projection: up to a 180 degree field of vision can be captured. However, the final photograph looks highly distorted and looks like a photograph of the scene as if reflected on a silvered ball. It may be that the name of this type of lens comes from what one imagines a fish sees under water, or that the image is distorted around a central point much like what a fish eye looks like.

Long-focus

A long focus lens is any fixed focal length lens that is longer than a normal lens (focal length is longer than the diagonal measure of the film or sensor). This includes the common sub-type, the telephoto lens, which uses special optics to compress the length of the lens.

These lenses bring the subject in by magnifying the subject and isolating it in the viewfinder. Lenses of this type are very useful for sports and wildlife photography for their ability to isolate a subject. However, these lenses have a drawback in that they typically are poor for low light use. Most long-focus lenses have a maximum aperture of only f/4, thus not permitting much light to reach the film and causing the use of slow shutter speeds to get correct exposure. In doing so, the photographer runs the risk of blurring the image due to his or her own movement.

One thing to bear in mind, try not to handhold your camera while using a shutter speed lower than that of the focal length of the lens being employed. This will help to assure sharper images. Using a sturdy tripod and a remote release will help a lot in low light photography.

Zoom

Zoom lenses are multi-focal length lenses. A fixed lens (or 'prime' lens) has one focal length descriptor (e.g. 55mm). Zoom lenses cover a range of focal lengths (e.g. 35-105mm). A zoom lens can thus be adjusted to act as a wide angle lens all the way through to a telephoto lens.

The disadvantage of zoom lenses is that the focal complexity and number of lens elements required to achieve a range of focal lengths is much greater than for prime lenses. This is becoming less of an issue as lens manufacturers achieve higher standards in lens production. This has allowed zoom lenses to produce pictures of a quality comparable to that achieved by lenses with fixed focal length. Another disadvantage of zoom lenses is that the maximum aperture (the speed) of the lens is usually lower. This makes inexpensive zoom lenses hard to use in low-light conditions without a flash.

Macro

Macro lenses have the capability to focus objects that are very close to camera without distorting the image. Generally any lens that has a magnification of 1:1 (life size) or better at its minimum focusing distance is referred to as a macro lens.

Tilt/Shift (TS)

Also known as Perspective-control (PC) lenses, these lenses allow the correction of image geometry. This is most useful when the film plane is not parallel to the surface of a subject, and the subject would otherwise be rendered with converging lines (lines parallel in reality are rendered converging). The classic example is when the camera is tilted upwards to photograph a building. The effect of converging lines is often unwanted and can be avoided by using a perspective control (PC) lens. It provides a function that is usually only available in view cameras: the lens can be shifted out of the optical axis (in the above example: upwards) and thus the recording media can be positioned parallel to the subject (the camera ponits orthogonally towards the building) and the subject is rendered undistorted.

Shift lenses are mechanically and optically more complex than ordinary lenses, don't provide autofocus and are comparatively expensive. They are often wide angle lenses and in this case frequently used in architecture photography. Longer lenses are often used in product or advertising type studio photography.

Catadioptric

A catadioptric, or mirror lens, makes use of mirrors to reflect light back and forth though the glass elements with the second convex mirror element acting as a negative lens, further extending the light cone. The result is a dramatic decrease in the length of a lens whilst still maintaining a larger focal length. Mirror lenses create tell-tale doughnut shaped highlights when a light is located in an area of the photograph that is out of focus.

Soft-focus

A lens that renders the image a little softer (i.e. less sharp). This is sometimes used in portrait photography to conceal minor defects in the skin of the person. To suit this purpose soft focus lenses usually have focal lengths around 80-100mm (fFor 35mm cameras) most popular for portrait work.

Fisheye

A fisheye lens (mounted on a Nikon SLR camera)

The term 'fisheye' was coined in 1906 by American physicist and inventor Robert W. Wood based on how a fish would see an ultra-wide hemispherical view from beneath the water (a phenomenon known as Snell's window). Their first practical use was in the 1920s for use in meteorology to study cloud formation giving them the name "whole-sky lenses". The angle of view of a fisheye lens is usually between 100 and 180 degrees while the focal lengths depend on the film format they are designed for.

Mass-produced fisheye lenses for photography first appeared in the early 1960s and are generally used for their unique, distorted appearance. For the popular 35 mm film format, typical focal lengths of fisheye lenses are between 8 mm and 10 mm for circular images, and 15–16 mm for full-frame images. For digital cameras using smaller electronic imagers such as 1/4" and 1/3" format CCD or CMOS sensors, the focal length of "miniature" fisheye lenses can be as short as 1 to 2mm.