Typically, the capacitor between and very close to the two power pins is an absolute requirement, unless the manufacturer specifically states otherwise. Unless otherwise recommended, I add a capacitor from ground to the power pin that is the reference point from which the output voltage is determined. For a 741, that is the negative power pin, since the output voltage originates at the collector of an NPN transistor after the current mirror from the differential input stage. Since bypass capacitors are cheap, it probably doesn’t hurt to bypass the positive power pin to ground as well, supplying the suspenders to complement the belt.
Analog Devices has good app notes on this topic.