Just wondering if there are any cameras that are specifically used for taking photos at night or in near complete darkness?
Modern full-frame sensor cameras are pretty amazing at this. The Nikon D4 for example can shoot at up to ISO 204000, yes 204 thousands! One reviewer said he was shooting subjects which he could not see with his own eyes, yet the camera focused and exposed properly. The key is that those cameras, like the Canon 1D X and Nikon D3S have big pixels which are extremely sensitive to light.
All cameras require some amount of light, after all the word photography comes from Greek and means drawing with light. A handful of cameras cheat by adding their own infrared light to the scene and measuring that. The result is a grainy monochrome image. All such cameras that I know are made by Sony and that feature is called NightShot but I have not seen one of these for a few years. It is much more common in camcorders than still cameras.
All you need is a tripod.
This was taken at ISO 500, f/4.5, and 25s:
It was about 35 minutes before sunrise. That's Phantom Ranch, at the bottom of the Grand Canyon. The only thing I could see to focus on was the bright light. In fact, I couldn't even see the other lights with my naked eye. Everything else was completely black to my eye.
In addition to @Itai, many, if not most, cameras are designed to shoot at night with long shutter speed settings or by using
Bulb mode to hold the shutter open manually letting more light in. Of course, moving objects will be blurred. There are also lenses with very large maximum apertures that aid low-light shooting at faster shutter speeds such as the 50mm Leica f/1 Noctilux, f/0.95 Noctilux, and the Voigtlander f/1.1 Nokton. This page on Luminous Landscape talks about such lenses some more.
In addition to "any camera using a tripod and long enough exposure time", there are also specialized cameras that can form images from infrared (heat) radiation: http://en.wikipedia.org/wiki/Thermographic_camera
Thermographic cameras don't need visible light at all. I guess it's a matter of definition whether you would call the result a "photo".