Lenses are categorized by their focal length in mm. More or less that number relates to angle of view which dictates the ideal use of a lens.
Lenses that have an angle of view somewhat similar to human eyes are called normal or standard lenses. This is around 35mm for crop sensor dSLR's or 50mm for full-frame dSLR's and (35mm) film SLR's. Normal lenses are great for taking people in general. You use it also for portraits, candids, pets and most anything that interests you.
Wide angle lenses see more than normal. This makes the objects in the picture smaller but the scene wider. Less than 25mm to around 12mm are considered wide angle in crop sensor dSLR's while around 35mm to around 18mm are wide for full-frame and (35mm) film SLR's. These lenses are very good for taking landscapes and large group shots.
Super wide angle lenses are those that have lower than 12mm for crop sensor dSLR's and lower than 18mm in full-frame and (35mm) film SLR's. These lenses have pronounced distortion making straight lines curve inwards. The best example of this is the fisheye lens. Aside from special effects, super wide angle lenses are used for cramped spaces. You can see more without backing away too much.
Telephoto lenses have a narrower angle of view than normal lenses. They usually range from 50mm to 100mm for crop sensor dSLR's and 75mm up to 150mm for full-frame and (35mm) SLR's. Subjects appear bigger to fill up the picture more easily. Lenses like these are good for closeup shots where you focus more on detail.
Super telephoto lenses are used to pull very far objects closer to you. They are those with focal lengths higher than 100mm for crop sensor dSLR's and more than 150mm for full-frame and (35mm) SLR's. Super telephotos are important in wildlife, nature and for sleuthing.
Prime lenses vs. Zoom lenses
Lenses that have only one focal length are called prime lenses. They do not zoom. An example is the 50mm lens below. Those that have variable focal lengths are called zoom lenses. Zoom lenses are indicated by their minimum and maximum focal lengths like the 18-55mm.
Generally, prime lenses have better optical quality than zoom lenses. That's the reason you will find that most demanding professional photographers use prime lenses exclusively.
Zoom is the ability of the lens to change focal length. There are wide zoom lenses like the 10-20mm, standard zoom lenses like the 18-55mm or 28-75mm, telephoto zooms like the 80-200mm and 100-300mm and super zooms like the 28-300mm and the Tamron 18-250mm.
(X) Zoom Factor Computation (and the insignificance of it)
To compute for the zoom factor of a lens, use the following formula:
Zoom factor = maximum focal length / minimum focal length
An 18-55mm zoom lens will be computed as 55/18 resulting to 3X. The 18-250mm super zoom lens can be rounded to 14X. That is very high for dSLRs. The longest at the time of writing (9/2012)is the Nikon 18-300mm 16.67X zoom lens. It's harder to make large zoom factor lenses for dSLRs due to cost and physical constraints.
Zoom does not equate to magnifying power. Take note that a 1000mm non-zooming lens (1000/1000 = 1X) will make a far object seem exactly four times closer to you than that 14X 18-250mm super zoom. It's all in the focal length.
Focal Length / Angle of View Comparison
Aperture, Lens Speed
When buying lenses, you may also be concerned with speed. Aperture is the size of the hole. It is indicated by f/values. The lower the f/number, the larger the maximum aperture size of the lens, the faster you can set the camera's speed and take the shot, the faster the lens is but the more expensive it becomes. F/1.8 is fast enough and affordable, f/1.4 is great, f/1.2 is heaven while f/0.7 is mind-blowing. These very large aperture sizes will produce very shallow depth of field (DOF) making blurry backgrounds easy as pie. They also make shooting in low light a lot easier. You can usually find these low f/numbers with (but not limited to) 50mm lenses.
With some zoom lenses, the maximum aperture may also come in a range like the 18-55mm f/3.5-5.6. That's just the maximum aperture in the focal length range. The minimum aperture is different and usually not indicated in the naming of the lens. Those kind of zoom lenses are referred to as "variable aperture" zoom lenses and aperture size changes as you change focal length. There are faster (meaning wider aperture) and more expensive (yes, more pricey) zoom lenses that don't change aperture size as you change focal length. They are called "constant aperture" zoom lenses.
Special Purpose Lenses
There are some specialized lenses for different purposes. If you are concerned with making very small objects seem large, you will need a macro lens. Most macro lenses are normal or telephoto. Check the minimum focusing distance when buying a macro lens to suit your needs.
Another specialized lens is the tilt-shift lens. This is usually a wide angle lens that has controls to move the mount sideways and up or down to allow optical correction for maintaining straight lines. This is very important for architectural shots. On this picture on the right, the left side is uncorrected while the right is with tilt-shift applied.
The Kit Lens
Believe it or not, the 18-55mm kit lens is enough for most of the common shooting conditions you will encounter. The 18-300mm 14X zoom lens might be the lens with longest zoom range in the dSLR world but it definitely is not the best in glass quality. Optically, the best lenses are those that don't zoom. To zoom non-zooming lenses, the secret is to use your legs. Walk.
Digital sensor size will play a role on the angle of view of a lens. Canon crop sensor dSLRs have a crop factor of 1.6X while Nikon, Sony and Pentax have it at 1.5X. The smaller sensor size changes the angle of view of the lens compared to a 35mm film camera or a full-frame dSLR by the crop factor. This means that on a 1.5X crop sensor dSLR, the 50mm lens will act like a 75mm lens on a full-frame dSLR.
50mm x 1.5 = 75mm
Take note that the 50mm lens is still 50mm on the crop sensor dSLR. The only difference is that it's angle of view on the crop sensor dSLR is equal to the angle of view of a 75mm lens on a full-frame dSLR or a 35mm film camera.
This is important to those who are used to film SLR focal length terms. If you are just starting, you shouldn't have any problem unless you use mixed full-frame and crop sensor bodies. You only need to remember what is the normal focal length of your camera, 35mm for crop sensors and 50mm for full-frame. Lesser than that number is wide angle while more than normal is telephoto.
On a side note, I have to mention 35mm film because there are other film sizes. Do not confuse it with a 35mm lens. 35mm film is the standard reference for comparison. This is what is referred to when you read "Equivalent" under focal length in some spec pages.
Now you know!