Voltage Regulation and Capacitors
Many regulators will oscillate if the capacitor on the output is omitted, or if it is too far from the regulator, and not regulate properly. I've actually seen this happen: a friend of mine copied a power supply design of mine, left off the output capacitors on the regulators, and found that one of them was only delivering a couple of volts. The data sheet will have details of the capacitors that are required.