Three-terminal linear regulator output capacitor selection
It depends entirely which linear regulator you are using. The datasheet for a good one should tell you specifically what output capacitor is required or if that regulator will be stable without one. In some cases there might be upper and/or lower limits on the equivalent series resistance (ESR) of the capacitor used, and this will also be spelled out in the datasheet.
But there is no general rule --- you must read the datasheet of whatever specific regulator you are using to find out if that type requires a capacitor, and what capacitor parameters are required.