I am installing recess lights in my living room (20' x 17'). The old ceiling has been demolished, so the installation is relatively easy. My question is: How far apart should I space the lights to have adequate general purpose lighting in the room?

Generally speaking, the spacing is done as a ratio to the ceiling height, anywhere from .75:1 to 1:1, but this depends on the actual lamp, and the light output and beam spread of the lamp, and the photometrics, (How a fixture distributes light), of the fixture, along with the reflectance of the wall, floor and ceiling surfaces

So, if you are using a 65R30 flood lamp, and ceiling height is 8 foot, a reasonable layout would be 6 foot spacing.

If the lamp is larger than 65 watt or equal output, then 8 foot spacing would work.

This is a brief example. Lighting layout is, or can be, complicated to understand, and even worse to explain.

Here is some reading you can review:
http://www.lightingfacts.com/Recesse...20spacing.html
http://www.forteelectric.com/Howtolayoutcans.html

There is a great deal of information available that explains further the variables involved with lighting, that I just cannot fit here.

If this helps, great, if not get back and we can continue.

With the ever increasing price of electricity, look at other than the conventional incandescent lights. Some of the metal halide lights produce an attractive white light using much less electricity that even fluorescents. Look for fixtures that spread the light out so you don't alternating bright and dim spots. They are much more expensive to instal, but save money over the long run. The bulbs last almost forever. You may need to get into a lighting specialty store.