The corner frequency depends on the specific op-amp, and information about frequency response can be found in the manufacturer documentation. For the 741 op-amp, open-loop roll-off starts around 10 Hz, but closed-loop roll-off may start at kHz or so (see Eggleston Fig. 6.17).
Yes, it can matter a lot if you are feeding high frequency signals into the op-amp. Attenuation of high frequencies can distort a signal that has sharp features (the Fourier components that make them up get killed).