Regulated means just that. It indicates that the supply will not change appreciably in voltage output, regardless of the load placed on the supply (if operated within the specifications of the regulating element, of course). There are many types of power supplies out there, and some which are designed for specific equipment may put out voltages higher than indicated in their documentation, and rely on the load to bring the voltage down to it's operating levels. LED's don't typically put enough of a load on these supplies to do this, so the result is higher voltages than specified on the supply and more current flowing than is safe for the LED.
Always use a regulated supply when powering LED's where the current is limited by a resistor. PC supplies are fine, as they are a regulated power source.