I would say that it is definately not necessary to run an airpump all the time. However, for some setups using one may be advisable. In a planted tank you generally want high co2, so an air pump would not be a good idea as it drives off dissolved gasses.
If your tank is very heavily stocked, to the point where your fish are gasping at the surface when no airpump is running, then you should probably use one(or cut back on stocking). Of my six tanks only one has an airpump and mostly because I like the bubble curtain effect in that tank. I have unplugged it for weeks with no ill effects.
If you need surface agitation but don't want the airpump you could always position the output from your filter so that it splashes into the tank.