As a general rule of thumb, in the modern DSLR world that is primarily dominated by Canon and Nikon, focal lengths are stated at their "when used on 35mm/full-frame body" values. Focal length is focal length, and doesn't physically change when the imaging medium changes in size, however different sizes of film or sensor do change the effective angle of view that is actually captured. Focal length is a rather useless value, all things being equal, as it doesn't really tell you much of anything about what the lens will do when used on a particular camera. The angle of view is a considerably more useful value, but that can be difficult to calculate given the factors involved. A simpler solution is to determine the angle of view "bucket" that your lens falls into for the size of sensor you are using.

On Focal Length, Angle of View, and Sensor Size

The angle of view of a lens of a particular focal length is dependent on the size of the imaging medium. On on a 35mm sensor or film (full-frame sensor, such as what you get with a Canon 1D or 5D, the Nikon D3's), an 18mm DSLR lens is a wide-angle lens. Full-frame bodies are expensive, and most DSLR's come in a variant of APS-C, or cropped-sensor, sizes. Most APS-C sensors are around 22-23mm. The smaller sensor captures less of the image circle projected by the lens, which effectively reduces the angle of view. While the lens is an 18mm focal length lens, on a sensor that is smaller than 35mm, the lens "behaves" as though it is a longer focal length. As such, the focal length ranges that determine if a lens is wide, normal, or telephoto change with the size of the sensor.

Common Fields of View @ 35mm

There are some common fields of view, assuming a full frame (35mm) sensor, that can be used to generally group focal lengths. There are slightly differing schools of thought on this, however here is a table from a well-known source, DPReview.com:

Focal Length        Angle of View Bucket
----------------------------------------
< 20mm              Super Wide Angle 
24mm - 35mm         Wide Angle 
50mm                Normal Lens 
80mm - 300mm        Tele
> 300mm             Super Tele

(From dpreview.com: Focal Length)

According to Wikipedia, a "wide-angle is a focal length substantially shorter than the focal length of a normal lens." A normal focal length is one which closely matches the diagonal of the image medium. In a full-frame 35mm sensor body, the sensor is 36x24mm, which is a diagonal of 43.3mm. The closest common "normal" focal length used by most manufatrurers is 50mm, which is pretty close to the 43.3mm diagonal of a full-frame sensor. (Similarly, in large-format photography, the film size is 4"x5", or 101.6x127mm, which has a diagonal of 163mm. With 4x5 cameras, a "normal" focal length lens is usually around 150mm.) While the term substantially in the Wikipedia article is not well-defined, the Wikipedia article cites 35mm and less as "wide-angle" and "ultra-wide-angle". Similarly, focal lengths substantially longer than a normal lens are "telephoto" through "super-telephoto" lenses.

Crop Factor and Angle of View

Since the field of view buckets that a lens falls into are dependent on focal length, and effective focal length is dependent on sensor size, one most first determine the effective focal length on a sensor smaller than 35mm. An easy rule of thumb can be used to calculate the effective focal length: Divide the diagonal of a 35mm sensor by the diagonal of the actual sensor, and multiply the resulting number (the "crop factor") by the focal length.

cropFactor = fullFrameDiagonal / croppedSensorDiagonal
effectiveFocalLength = actualFocalLength * cropFactor

This assumes you know the diagonals of your camera sensor. The diagonal can be computed fairly easily using the Pythagorean Theorem if you know the width and height of the sensor. Pythagoras' theorem quite simply states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

This translates into the formula:

a^2 + b^2 = c^2

A sensor, cut in half along its diagonal, is a right triangle, and the length of the diagonal (c) can be computed as such:

diagonal = sqrt(width^2 + height^2)

If you know the dimensions of your sensor, and are not afraid of a little math, you can computer the effective focal length of any lens on any camera body, and once the effective focal length is known, determine whether it is ultra-wide, wide, normal, tele, or super-tele. As it is unlikely most people will know their sensor dimensions, here is convenient a table of sensor sizes, diagonals, and crop factors:

Sensor                   Crop Factor     Diagonal      Width      Height
-------------------------------------------------------------------------
4x5 Large Format Film    0.27            162.6mm       127mm   x  101.6mm
Digital Medium Format    0.64            67.1mm        53.7mm  x  40.3mm
Full-Frame               1.0             43.3mm        36mm    x  24mm
Canon APS-H              1.26 (1.3)      34.5mm        28.7mm  x  19.1mm
Pentax/Sony/Nikon DX     1.52 (1.5)      28.4mm        23.7mm  x  15.6mm
Canon APS-C              1.62 (1.6)      26.7mm        22.2mm  x  14.8mm
Sigma Foveon             1.74 (1.7)      24.9mm        20.7mm  x  13.8mm
Four Thirds              2.0             21.6mm        17.3mm  x  13.0mm

As an example, to demonstrate and prove the concept. The Canon APS-C sensors have a crop factor of 1.6x (most commonly stated, more accurately, 1.62x). This is calculated as follows:

cropFactor = 43.3mm / 26.7mm = 1.6217228...

APS-C Effective Focal Lengths

Now that you know the crop factor of common sensor sizes, you can compute the effective focal length of any lens you may use. Assuming the 18mm focal length of the original topic, its effective focal length on a Canon APS-C sensor (i.e. 550D, 60D, 7D) would be:

effectiveFocalLength = 1.6 * 18mm = 28.8mm, or 29mm

You can compute the focal range of a zoom lens just as easily. Given the Nikon 14-24mm lens:

shortFocalLength = 1.5 * 14mm = 21mm
longFocalLength = 1.5 * 24mm = 36mm

Full Frame vs. APS-C Angle of View Buckets

The most common sensor sizes for many of the most common DSLR cameras are Full Frame and APS-C. We have a table of angle of view buckets for full frame, so it is useful to compute a table that defines the angle of view buckets for APS-C. I've used a crop factor of 1.55 to cover Canon APS-C and Pentax/Sony/Nikon APS-C:

Focal Length        Angle of View Bucket
----------------------------------------
< 12mm              Super Wide Angle 
15mm - 23mm         Wide Angle 
32mm                Normal Lens 
51mm - 200mm        Tele
> 200mm             Super Tele

Given the two AoV bucket tables, we can arrive at a table of common lenses and their AoV's for both Full Frame and APS-C sensors:

FF Focal Length   FF AoV                 APS-C Focal Length   APS-C AoV
--------------------------------------------------------------------------------
8-15mm            Super-Wide          |  12.4mm-24mm          Super-Wide to Wide
10-22mm           Super-Wide          |  15.5mm-34mm          Wide to Normal
14-24mm           Super-Wide to Wide  |  22mm-37mm            Normal
16-35mm           Super-Wide to Wide  |  25mm-54mm            Normal to Tele
24-105mm          Wide to Tele        |  37mm-163mm           Normal to Tele
70-200mm          Tele                |  108mm-310mm          Tele to Supertele
100-400mm         Tele to Supertele   |  155mm-620mm          Tele to Supertele
--------------------------------------------------------------------------------
14mm              Super-Wide          |  22mm                 Wide
24mm              Wide                |  37mm                 Normal
35mm              Wide                |  54mm                 Tele
50mm              Normal              |  78mm                 Tele
100mm             Tele                |  155mm                Tele
135mm             Tele                |  209mm                Supertele
300mm             Supertele           |  465mm                Supertele

Visual Examples of Focal Length and Angle of View

I'll try to take some example photographs when it is light again to demonstrate the differences between super-wide, wide, normal, tele, and super-tele. (Its too dark right now to get any decent shots outdoors, and indoors I don't really have enough space to get telephoto/supertelephoto shots.)