Lots of people buy advanced cameras (such as the Sony NEX-7) because they're fast: They're great for taking action shots in sports, for instance. But some cameras are including special scene modes that do the opposite of freezing the action: They leave the shutter open long enough so that moving lights in the scene appear in your images as long trails of light.
For example the superzoom Samsung Galaxy Camera has a mode called Light Trace, which leaves the shutter open as long as 15 seconds. You can experiment using a flash light by drawing an image in the air or writing your name.
Other cameras have similar modes: One is called Fireworks mode, for example, and leaves the shutter open several seconds, letting you achieve those fireworks photos that look like dripping fountains of light. To get the best results in such modes, make sure to place your camera on a stable surface or use a tripod.