Light is your greatest ally. But that doesn't mean you want to do your slow shutter shooting in bright sunlight -- in fact, it means the opposite. The most awe-inspiring slow shutter speed photographs harness the visual power of bright light against a dark background. We all know light moves very fast, but we can't really experience "seeing" light move. Shooting bright lights -- such as hand-held LEDs or car headlights whizzing along a busy highway -- at night lets us visualize light in motion.
Even if you don't plan on waving around lights or turning a brightly lit Ferris wheel into a work of art, shooting at night allows for other artistic types of photos. Remember, the longer the shutter is open, the more light the camera sensor is exposed to. A long exposure, which lets in a great deal of light, can make a picture taken on a moonlit night look like daytime. Minimal lighting can provide enough color saturation for a vivid photograph while the slow shutter speed creates interesting motion blur you can't get with faster shutter settings.
Of course, it's possible to shoot with slow shutter speeds during the day -- you just have to take care to reduce the amount of light reaching the image sensor or risk blowing out the picture. A smaller aperture or lens filter can prevent photos from becoming overexposed.