The quality factor (Q) serves as a measure of a reactance purity. The Q is measured as the ratio of the energy stored in a component to the energy dissipated by the component. It should be noted that Q of the L-C circuit is defined at circuit resonance. If the circuit reactance is plotted as a function of frequency, the slope of the reactance at resonance is a measure of Q.
It depends on the circuit. All practical inductors have a maximum self resonant frequency with a certain Q at resonance. This resonance frequency is determined by inductance and parasitic capacitance at self resonance. A particular inductor is only useful as an inductive element below this resonance. Since Q is proportional to L/R and both series inductance and resistance can be frequency dependent, Q can vary with frequency. This is especially true for cored inductors and transformers. So the prudent thing to do is to measure Q over the frequency range of interest of Your circuit. This is easiest to do with an network analyzer, as previously pointed out. I usually use a HP4195 with an component adapter that directly gives a curve of Q and other parameters vs. frequency.