Generally speaking, most DSLR cameras these days are 14-bit. Smaller form factors may have lower bit depths, such as 10 or 12. The bit depth of a camera ultimately refers to the number of distinct levels of luminance a camera is capable of producing. This is a two to the power of factor, which means a 14-bit camera is capable of producing 2^14 or 16384 distinct levels (of tone...irrespective of color). A 12-bit camera is capable of producing 2^12, or 4096 levels.

A difference in the number of tonal levels has a small impact on the number of colors produced, and in most cases one would probably have a tough time telling the difference in color between a 12 and 14 bit camera. An increase in the number of tonal levels can have a significant impact on the overall quality of tone, particularly quality of gradients, in a photograph. A 12-bit camera is going to run a higher risk of producing photos with posterization, an effect that usually shows up in large areas of smooth grades or mostly solid color, due to sharp transitions in luminance.

When it comes to color, this can be more affected by the construction of the sensor, particularly the strength and quality of the color filters over each pixel in a bayer sensor, or the ability of a layered sensor to distinctly discern the number of electrons registered for blue, green, and red readouts from each pixel. A camera with a strong CFA (color filter array) will generally produce richer, more accurate color than a camera with a weaker CFA. The color quality, or color fidelity, of a camera is often more dependent these days on the capabilities of its image processor, or the precision and accuracy of the tone curves (picture or image styles) applied during the processing of the sensor signal. Even with a weaker CFA (which tends to make a sensor a little more "color blind"), color quality can still be tuned and improved with a high quality, accurate image processing algorithm. This applies more to JPEG than RAW, and when it comes to RAW the color fidelity story is again a bit more dependent on the ability of the sensor to sense accurate color.

So, in general, small and even larger changes in bit depth will generally not affect the overall perception of color in a photo. Humans, according to most studies, can only really see discern a few million distinct "colors" (at a constant medium illumination...when factoring in luminance, humans can detect trillions of levels of gradation for a given color...such as red or blue...but we are still only sensitive to a few distinct colors). A 10-bit device can handle over a billion colors (both "chrominance" and "luminance"). A 12-bit device can handle 68 billion colors. A 14-bit device can handle 4 trillion colors. Most people would be hard pressed to tell the difference between an 8-bit and 10-bit computer screen. Even fewer people could tell the difference between a 10-bit and hypothetical 12-bit display, and those who could would likely note the improved quality of tonal gradations more so than any perceived increase in observable colors. The value of a camera that produces higher bit depth photos is in the quality of tone...the quality and fineness of small differences in luminance between pixels. When it comes to color...so long as you have control over the low-level RGB tone curves applied to a RAW image when it is rendered, you could technically achieve any level of color fidelity you wished with just about any camera.