How to intelligently degrade or smooth GIS data (simplifying polygons)?

Question

I have detailed US county maps, from the TIGER LINE data sets. How might I sample, smooth, or degrade the data so that I get straighter, more boxy, less \"noisy\" shapes to

Answer 1

Answer by @unmounted is correct, but I would like to add one more suggestion.

Always use function ST_SimplifyPreserveTopology instead of ST_Simplify in PostGIS. Both use the same underlying algorithm (Douglas-Peucker), but the former avoids any simplifications which would result in invalid geometries. For example, ST_Simplify may result in geometry which intersects itself.