How much important is quiescent current while selecting Regulators?

Some voltage regulators operate best with a small load; without any load they may be unstable. An estimated 1-5% of the full load is advised.

its importance is to the cost of your application, Eg el cheapo 78L05 has quiescent current of few milliamps,
and if that is of no concern to your power supply source, then thats fine.
If battery operation then such current wastage is of concern, and you may then choose say LP2950 and your
cost goes up too.

for stability, all require a capacitor on the output, see specs. IMO there is no need for some power wasting
load to keep it stable...just choose the correct device.

So low quiescent current application comes only the place where we need to save power, like Battery powered applications.And the quiescent current increases as the load and current requirement increase.I think I will not get same quiescent current spec with higher load compared to smaller load.

quiescent is nothing but regulator operating current, means regulator itself consumes more current , even when load in off condition power consumption will increase without the utilization of the load. especially it is important in battery operated applications only, at the same time cost of the regulator also increases but power consumption will be reduced. that is purely based on application and budget requirements.