I use some fake directional-based ambient lighting. This is what it looks like in my voxel engine. The idea came from this article on image-based ambient lighting but I kept it more simple and instead am just using the six sides of a cube to gather lighting.
It's a simplified version of what Swiftcoder posted. The sides facing the skydome have different tints of color which change during the day/night cycle, as well as the intensity of the light bounce (how much they contribute to the final color). The sides facing the bottom are less saturated versions of the top colors. I only did this because the voxel lighting will block most of the light from the bottom sides anyways.