I have a variety of professional backdrops to use including: Black, Grey, Brown, Blue, Red, and White.
Dark grey is a very neutral non-distracting color choice and is very versatile. It also happens to be very popular today. Headshots for business purposes generally look good with light grey or white backgrounds.
White is a good choice for business headshots because it is the most consistent color when you are adding images to rosters at different times. A potential problem with white backgrounds is that they are often shown on computer screens that are also white. This can cause the background to "disappear" into the screen and leaves an unnatural and perhaps uncomfortable "floating head" type of look. This can be somewhat remedied by using a dark border around the headshot to create some separation.
For business headshots, colored backgrounds may vary in intensity and can look "off" when a directory or roster of images is viewed all at once. However, they can be a better choice than white if they are viewed individually on screens since they provide their own separation from the white computer screen background.
For portraits, colored backgrounds can be a good choice to match with a theme or to coordinate within the room in which the portrait will be displayed.
Areas of contrast tend to draw the eye of the viewer. Dark backgrounds tend to cause the viewer to focus on lighter areas of an image and light background tend to cause the viewer to focus on darker areas of an image. If you are being photographed in front of a dark background you should wear clothing that is somewhat lighter than the background but in a complimentary color. For example, using a dark brown background, wearing lighter colored clothing that has brown tones will look best. You would not want to wear a color that clashes with the background. If you are being photographed in front of a white background you should wear darker clothing and since white is neutral most any color clothing will work.
Another option is to use the environment as the background. This can be done where the background is sufficiently "blurred" so that it does not distract the viewer from the face but still gives a subtle clue as to the environment (i.e.: office setting, medical services, construction, countryside, etc.).