As Ralph mentioned, many people will avoid a bright white to avoid having a mat that is brighter than the whites in the image. In general, I will use the bright white but I like high contrast and deep saturation in my colors so I also like the frame and mat to be high contrast but that is my personal preference. If I am doing soft pastels, sepia tone, or low contrast black and white, then I will definite go with a less bright white mat such as the Bainbridge “photo white” mat which is good general use white for photography…thus the name.
Black is another commonly used mat color, but it is not as safe as white. My companies largest selling mat colors are by far white, with the slight off white and the bright white both selling in high quantity. One thing I have noticed is that most large orders will tend to be colors like photo white which indicates that it is mostly more professional people ordering it.