I'm working on a program that requires a dark interface, because it's mostly used in dark rooms. After some thought I decided to add a light version too and let the user swap them, but both still have the same requirement: They need to be very kind to the eye, because we are talking about many hours inside a dark environment.
What are good colors (both light and dark) to avoid eye fatigue/strain?
As mopsyd mentioned, just stay away from high contrast between your foreground and background. High saturation colors should be used sparingly as well. They are best when used for critical action or navigation items. Despite the great scientific stats behind it, I think mopsyd's red recommendation is a bad idea: too much saturation.
Working from that perspective, a combination of dark and light greys or neutrals is a good general starting point.
Here's a range of warm greys that work well. Warm tones tend to have a more calming presence that may or may not be necessary.
I think mopsyd is inferring a bit much from his very accurate explanation of the color spectrum. I have never seen anything that indicates warm tones on screen producing less eye fatigue. Cool greys can work just as well and may be more fitting for your branding.
Here's a very simple palette that gives you good range with just five colors. You have a nice dark and light neutral tone (I might go a touch lighter) and some vibrant monotones for contrast/emphasis.