Typical use cases:
1. Powering a breadboard. Probing with oscilloscope might be grounded, but that's a momentary contact, and at the same ground anyway (give or take ground loop, which is only important for sensitive circuits). Ground the 'common' side of the supply.
2. Testing or operating an audio amplifier. The signal input will most likely be coming from a grounded system (e.g., computer audio out), and the supplies may be bipolar or floating with respect to ground, preventing either side being directly grounded. You don't need a ground in this case, or ground can optionally be connected with a third cable (as noted).
3. Powering a floating circuit. Suppose you are testing a circuit where an isolated section requires power, and which is intentionally elevated from ground (an example might be a gate driver circuit, which is referenced to either the switching node, or the supply negative, and where neither is common to the reset of the circuit). Direct grounding is impossible in this case. Connecting a third ground cable to the circuit's ground (wherever that might be) probably wouldn't accomplish much, either. (The circuit under test should still be grounded somewhere, at least if it's handling more than 42V.)
"Common" is most often the negative side of single supply circuits, or the middle supply of bipolar circuits. "Common" is just a convention, and doesn't have an absolute definition (because voltage is a difference by definition). Typically, a circuit is designed so that all its signals are with respect to common, so that power supplies, probes, meters, shields, etc. can all be used relative to common.
Note that most power supplies, function generators, etc. are not usually very good for use on rapidly varying reference voltages, like high side gate drivers. There is usually a substantial amount of capacitance, at least due to the capacitance between windings in the power supply transformer, but often including additional filtering (Y type) capacitors, especially for those that use switching power supplies.
Tim