Is it necessary to connect bypass capacitors to the power supply terminal of an op-amp?

It is necessary to connect bypass capacitors (also called decoupling capacitors) to the power supply (VDD) terminal.
Without bypass capacitors, an op-amp might malfunction or, in the worst-case scenario, suffer oscillation or other problems.
Capacitors have parasitic resistance and inductance, which are specified as equivalent series resistance (ESR) and equivalent series inductance (ESL) respectively in capacitor standards.
Because of ESR and ESL, capacitors exhibit frequency-vs-impedance characteristics as shown below.
It is therefore recommended to connect one high-frequency filter capacitor (0.01 μF to 0.1μF) and one low-frequency filter capacitor (10 μF to 100 μF) across the VDD and GND terminals.
The high-frequency filter capacitor, which is more susceptible to the effect of board wiring inductance, should be placed closer to the op-amp than the low-frequency filter capacitor.
The PCB traces to these capacitors should be as wide and short as possible to reduce the impedance of the VDD-bypass capacitor-GND loop.