As a rule of thumb, for designing simple circuits, which have things like potential dividers for reference voltages, NTCs, loaded MOSFETs for low frequency signal switching etc. what is a reasonable current to load such things with, so that there is minimal noise in the generated signal, but no excessive current demand from the power supply. (Assuming the thing the signal is connected to draws negligable (u/pA) current from the signal itself / switching times are not critical etc.)

Generally I figured around 1mA, but then for larger, battery powered applications all these 1mAs add up..

A couple of very simple (illustrative) examples:

 

You are asking a very general question for which there is no specific answer. You supply as much current as the load requires.
A general rule of thumb for voltage dividers, references, output drive current, etc. you allow for 10 times what the load requires. Thus when the load is applied the voltage should drop no more than 10% of the unloaded source.

Zener regulated supplies, 3-terminal voltage regulators, etc. are a different matter. Two times the load current is sufficient. That is because the regulator maintains the output voltage up to the max designed current. Note that zener regulators do not have a sharply defined zener voltage. The more current you give it, the higher up on the curve and more sharply defined you go.

Good thing that you mentioned "low frequency" switching. At higher frequencies, higher resistances coupled with inherent and stray capacitances will lengthen your rise and fall times.

If you are aiming for low power consumption, go with the highest resistance that the circuit will allow and then reduce it some (20-50%).

CMOS and MOSFET components are voltage driven, not current, as they have very high input resistance and low input currents (typically less than 1μA). Thus you can go for much lower than 1mA (50μA would work). Make sure that you provide a resistance across the gate to bleed the input pin when the signal is removed.

 

Generally I figured around 1mA, but then for larger, battery powered applications all these 1mAs add up..

If you're interested in minimizing power consumption, then this application note by Linear Technology's Jim Williams might give you some ideas. Though somewhat dated (1987), many of the principles and techniques Williams describes are still relevant today.