I don't usually change threads through the piecing process unless I go from a dark area to a very light area, then maybe I should. An example would be a log cabin that has a very dark fabric on half, then a white on the other side. The colors white, natural and light gray seem to be good for most projects. I figured this out after I bought all sorts of colors. I think they are going to become quilting threads.
I have been working on a Bali Wedding Star, pattern by Judy Niemeyer, for several months. The background is a light beige fabric and the rings are all sorts of colors....purple to red, light orange to brown, light green to very dark green, and all of it has been pieced with a thread that matches the background color. A dark thread could have been very visible on the light, but the light beige just seems to work.
One of the things that I do so I don't have to change threads for my different colors is to set my stitch length smaller. I found out when I was paper piecing, that the recommended length is 1.8 or 1.6 rather than the 2 to 2.5 for regular piecing. This tighter stitch doesn't show nearly as much as the longer length. It is harder to rip out, so I do have to be more accurate with my seams, but that isn't a bad thing. haha.