You can achieve fabulous effects when taking photographs at night or in other low-light situations. City skylines that are mundane and boring during daylight hours take on a special quality when the lights come on. When photographing buildings, use the "magic time" in the half-hour or so just after sunset and before total darkness falls (conversely, just before dawn). The sky takes on beautiful hues that enhance outlines of buildings, for example. First-rate real-estate photos are often taken at twilight, with warm house lights creating a cozy mood. Use a hose to wet the driveway and you have the added benefit of reflections.
You can "paint" with flashlights, car headlights/tail lights, flash units and other creative sources of light. Freeways provide great gold and red streaks. Try long exposures while zooming your zoom lens. Jiggle the camera around during long exposures. During long exposures have a friend (or yourself, using your self timer) move around in the shot for a fun ghostly effect. Trigger a remote flash (maybe with a colored gel on it) in the middle of this exposure for even more interesting looks. Experiment!
When photographing outdoors at twilight or at night, be aware of your white balance settings on your camera. You'll get better control and more interesting effects if you use a setting other than your "Auto" setting. A daylight setting at night will give the photo warm tones if most of your light source comes from tungsten lights. For street lights and other common scenic light sources, try a tungsten or fluorescent setting for a more natural look to the light. Mixed light sources (a sunset sky with fluorescent lights in the foreground, for example) can give some really interesting looks to your shot. Many professional photographers these days shoot using the RAW settings on their DSLRs and with computer post processing choose the light balance they want.
Often, you can get great creative effects by using the "B" shutter speed setting. This means you're triggering the shutter and then holding or locking the shutter open for whatever time span you want, whether it's 30 seconds or 3 hours. Not all cameras will let you do this, although most will let you shoot up to 30 seconds. When in doubt, bracket.
Digital photography has made this process even more creative and intuitive. Because you don't have to worry about film costs, experiment with different exposures, panned blurs and other creative techniques. Bracket, bracket, bracket!

The above photo was taken at ISO1000 using a Nikon D300 digital camera. Shooting Camera RAW, white balance adjustments were done afterward in Photoshop, although some of the golden glow was kept just for the ambiance of this night scene. Nik DFine was used to get rid of some noise in the image.
Tools That Help
Cameras that Handle High ISOs Easily
If you're trying to stop action at low light levels, you must use a flash (not always desirable because of its artificial look) or fast digital settings (ISO 400 or higher), which is very sensitive to light. Many less-expensive cameras start to show objectionable "noise" at ISOs of 400 or above. Noise can take two forms: luminance (which is sort of like grain/spots on film cameras) or color (shadow areas deteriorate into red, green and blue dots). Sometimes this can be fixed using noise reduction software, such as Noise Ninja, Topaz deNoise, Nik DFine or even the RAW noise reduction software tools in Adobe Photoshop CS5 or Lightroom 3.
Many higher-end digital cameras can shoot at ISO equivalents of 800 or even 6400,with minimal noise issues. Just understand that you may have quality problems so experiment to see what your camera will do BEFORE going out into the field.
One common fallacy in night photography is that photographers think they NEED these high ISOs. If you're shooting a static scenic using tripod and cable release, you'll get a better quality image at a low ISO, such as 100 or 200.
Fast Lenses
If you're doing a lot of low-light work, you may want to consider investing in a fast lens, which means that the largest aperture is VERY large, as in f/1.0 or f/1.2, thus giving you one or two f/stops more light, and hence faster shutter speeds. Typically, 50mm lenses are relatively fast and can be purchased for less money than their wide-angle or telephoto counterparts. Photojournalists, who must often photograph indoors using available light, use a combination of fast lenses and high-end digital cameras.
Spot Meter (either in-camera or hand-held)
This piece of equipment is not essential but does help.Night photography often has extreme, uneven ranges of light levels. Metering for such situations is difficult. If you choose to meter, keep in mind that you likely will NOT want middle gray tones; you want your night scenics to look as though they were taken at night, so they will usually be a couple of stops darker than what your averaging meter says. If you have a spot meter, take your measurements off important highlight areas, and use those settings. If you don't have a spotmeter, and if you're photographing a stage play, for example, try to get close enough for a few moments to get a reading, then use that reading when you're further away from the stage. If you don't have a spot meter, you can try using your longest telephoto lens (though hauling bulky photo equipment into a theatre may not be for everyone). For stage plays and other artificially lit situations, use the tungsten or (occasionally) fluorescent settings on your camera. Bracket if you can.
Tripod
A tripod is essential for much of this work. Get one with rock-solid legs. A high-quality tripod is one of best photographic investments you can make.
Cable Release
If you're making a long exposure not found on your shutter speed dial (on older cameras, this will be any exposure longer than 1 second; on newer automatic cameras, usually anything longer than 30 seconds), you'll need a cable release to hold the shutter open on its "B" setting. Otherwise, you can set your shutter speed and use the self-timer. Either a self-timer or cable release is essential for sharp night exposures unless you're after a experimental effect. To make your time exposures even sharper, momentarily block the light to your lens just as you trip the shutter and again as you end the exposure. The shutter release,which also makes the mirror lift on a 35mm camera, can cause camera shake.
Special Situations
Star and Moon Photography
If you want to get sharp photos of stars, moon and other celestial objects, keep in mind that you are contending with the rotation of the earth, so your celestial objects will leave a "trail" if your exposures are too long. Sometimes this is a desirable creative effect. How long can exposure times be before sky objects begin to "trail?" Try this formula: e=600/fl, where e is the maximum exposure and fl is the focal length of the lens. Some examples are: 12 seconds with a 50mm, 17 seconds with a 35mm, and 6 seconds with a 100mm. At twilight you don't have to worry as much about these "trails."
One great moon photo you can take is of a crescent moon in a dusk or dawn sky. Wait until the sky glow has decreased enough to allow the earthshine to show. This ghostly glow on the "unlit" portion of the lunar surface is caused by light reflected off the daylight side of the earth. You can best capture earthshine two to four days after new moon, starting 30 minutes after sunset. Take a light meter reading of the brightest portion of the sky, then open up one f-stop. For example, you might find optimum conditions at a light reading of 17 seconds at about f/5.6 to f/8.0 with a 35mm wide-angle lens at an ISO of 100. In twilight scenics that include a moon, you can use a split neutral density filter to hold detail in your darker foreground.Using Photoshop, you can substitute in RAW the graduated tool for the ND filter
If you want to photograph a bright, white moon high in the sky, using a shutter speed equal to 1/film speed, use f/16 if the moon is full, f/11 if gibbous, f/8 for half and f/4 for a slender phase of the moon, says one moon photography expert. Another recommends these "ball park" settings with ISO 100 film: crescent moon: 1/60 at f/4; half moon: 1/60 at f/5.6; full moon: 1/60 at f/8. So experiment, bracket, and note your settings. If you just want a bright photo of the moon and nothing else in the landscape, use the Sunny 16 rule (where is the light source on the moon coming from?...). Use at least a 200mm lens unless you want the moon to appear as a small bright dot. A 500mm or longer tele will reveal details.
You can also try time exposures of a landscape lit by a full moon. ISO 100 film pushed to 400 works for this kind of situation. Use the formula above, opening your lens up as much as possible. f/2 at 17 seconds using a 50mm lens is one formulation. Bracket.
Since you must often carefully plan your night exposures, it helps to know ahead of time where and when your celestial objects will appear. Many astronomy computer programs will give you the whereabouts of celestial objects. A local newspaper will give you sunrise/sunset times. If you don't have access to these computer programs, the Nautical Almanac, published by the U.S. Naval Observatory, is available in U.S. government bookstores and can be ordered directly from the Superintendent of Documents, U.S. Government Printing Office, Washington DC 20402. The Internet also has many valuable sources.Also, there are now apps for this sort of things for smartphones.
Star trails can be great fun. Since you want some definition of foreground, start your exposure while there is still a little bit of afterglow in the sky. Then you can leave your shutter open all night, even 12 hours (don't sleep in!). The tricky part is figuring out how much afterglow to use. One way to avoid the guesswork in this is to make a double exposure, taking the first exposure when colors are at their best and there is still enough light to meter accurately. Then simply wait until the sky has gone completely black, before opening the shutter again for your time-exposure phase. Take care not to move the camera between exposures or while winding. Compose the foreground of your photo when it's still light enough to see what's there.
Fireworks
Manually set your shutter to "B" and keep the shutter open about 8 to 10 seconds to record several bursts of fireworks on each frame of film. A starting point for exposures is f/8 with ISO 100 , f/11 with ISO, and f/16 with ISO 400 . Vary the f/stop or the number of bursts; you ever know the intensity of a fireworks until it explodes. Take plenty of shots because fireworks shows usually don't last very long.
Lightning
First, use common sense. This can be a very dangerous form of photography! Stay away from open areas, don't use a metal tripod and leave the area if the lightning is getting too close. You must shoot lightning at night or at very low light levels. Since you don't know exactly when and where lightning will strike, you must use time exposures. Start at 30 seconds and go on to several-minute exposures. Various lenses help, too. Kodachrome gives the most natural color, while Fujichrome and Elitechrome give a warmer look. Tungsten film will give lightning a slightly bluish cast. Foreground subjects, creating silhouettes, enhance composition. Expect to use a lot of film before you get any great images. Recently developed equipment includes sensors that can detect lightning in brighter conditions and hence trigger camera shutters.For more info: lightnighttrigger.com
Caves
Simple, easily transported equipment works well here. You'll need a good-quality backpacking tripod. Caves are often wet, so waterproof cases are essential. Moderately wide-angle lenses, such as a 35mm lens, capture the view nicely. Long time exposures permit the use of multiple flash units fired over a fairly long period of time. To light up large areas in caves, flashbulbs on folding flash guns work well. Strobes are ideal for good for close-ups and other single-flash shots. For the best results, keep in mind great composition and don't worry about even lighting; large areas of dark enhance the cave feeling. Sidelighting and backlighting create dramatic effects. For off-camera flash, use a "B" setting and have an assistant fire the flash.