Understanding RAW Files Explained

There is probably more misinformation, disinformation and lack of information regarding what raw files are all about than on any other digital imaging topic. There are also many reasons why one should shoot in raw mode, but also quite a few reasons why many people don't. Let's have a look at both.
What is Raw Mode?
When a digital camera makes an exposure the imaging chip (whether it's CCD or CMOS) records the amount of light that has hit each pixel, or photo site. This is recorded as a voltage level. The camera's analog to digital circuitry now changes this analog voltage signal into a digital representation. Depending on the camera's circuitry either 12 or 14 bits of data are recorded. Incidentally, if the camera records 12 bits of data then each pixel can handle 4,096 brightness levels (2^12), and if 14 bit then it can record 16,384 different brightness levels (2^14). (To my knowledge no current imaging chip records a true 16 bits worth of data).
Of course what happens after you've ...