If you are using a board without solder-mask (for example, a home-built board) keep plenty of clearance between soldered joints and the fill. On older PC board technology (solder mask over HASL) you would need to do a checkerboard pattern so the solder mask wouldn't fall off. The newer boards (solder mask over bare copper - SMOBC) this is not a problem and copper fills are no worries.
Having a similar copper density on both sides of a layer (layer pairs on multilayer boards) makes fabrication a bit easier, and reduces warpage when going through reflow soldering. These are mostly a worry for high-volume manufacturing.
After doing 4 or 6 layer boards with ground and power planes, it's really hard to go back to 1 and 2 layers!!!
-Dale
