I will consider this as my ignorance about the tool but I am not getting the results I was expecting.
Here are the setting for the Sky:
Here is what it looks like in Preview mode:
Here is what it looks like in the Editor and when the scene is baked:
What am I doing wrong? How can I get a single color background?
Settings in the Bake tab are used only for the lightmap baking and the preview.
The settings in the Sky tab are used for the presentation, to get a single color background you can set a small single color Sky texture in the Sky tab. If you would like such texture to be used also in Orbit and Top views, you can enable it in the Viewer tab.
Thanks - is there a particular size that you recommend?
I need to find some good 360 panorama images to use as backgrounds/skies. 
For a single color sky, you can use 1x1 texture. For panorama image 4096x4096 is recommended (you can set larger, but it will be scaled down to 4096x4096 anyway).
Thanks - worked great. Now I can use this approach on some future projects.
One other silly question though. If I want a panorama image, do I have to do something special to it so that it looks right as I rotate the scene or is any standard image in a 4096x4096 format going to work? If it needs to be a 360 degree image, does anyone have a suggestion for a good tool to create such an image?
It needs to be 360 equirectangular panorama, so there are no visible stitches (for example: http://hdri-skies.com/).
We always used ready panoramas, but if you have proper equipment, there are tutorials how to create them: http://paulbourke.net/miscellaneous/sphericalpano/
I am working on an exterior building rendering and have questions with the following, which seem to be related to the above thread but aren’t quite answered:
-I’ve added a sky texture, which shows up in the image box but disappears when I preview render.
-Because the building is the only structure in the rendering the sun is washing out the textures and colors in the render, even when I turn the sun strength all the way down.
-How do I get shadows? This is probably related to fixing the sun strength I assume?
Right, the sky texture is rendered only in the viewport. Preview is mainly for quickly checking if the scene is well-lit, and the sky texture is not rendered there because it does not influence the lighting.
What is usually too strong in exterior scenes is the sky, not sun. So, you should primarily decrease the Sky strength in the Bake tab: please try something between 0.5 a 1. Decreasing the Sun strengh is not that necessary - you can experiment with values from 4 to 8.
You are, right if you decrease the (sky) light strength, you will start to see shadows.
