The question "Do I need to use a regulated power supply with my xxx..." comes up occasionally. The following is an explanation of some of the characteristics of regulated and non-regulated power supplies.
This is where the output voltage varies with the mains voltage supply. Although Australia has a nominal 230Vac 50Hz power grid, the actual voltage arriving to your home varies. It can be anywhere between 220Vac and 260Vac depending on your location, time of day, etc. Since an unregulated power supply is not much more than a transformer (with a fixed input to output ratio), rectifier and capacitor, the output voltage will also vary with the input voltage. This is not too much of a problem in most cases as the variations are a fairly small percentage.
This is where the output voltage varies with the current drawn from the output. As an example, the output voltage of an unregulated 12V, 500mA PSU might be close to 12Vdc when you are drawing the full 500mA, but could rise to as high as 17V - 20V with no load. If the manufacturer of the connected device has used components with (for example) a 16V maximum voltage rating and the device only draws 100mA, the device may be damaged by the excessive supply voltage. The other issue is that the device may use an internal regulator to drop the 12V down to a lower voltage for part of the circuit. If the input voltage is considerably higher than specified, the regulator may (depending on its design) dissipate a lot more heat than it was designed to and be damaged or shut down unexpectedly.
Due to its very simple nature, an unregulated power supply may also have a lot of 50Hz (or 100Hz) ripple on the output. This is because the transformer and rectifier charge up a capacitor on every half cycle of the AC voltage. The capacitor attempts to hold the DC output voltage constant between cycles, but at higher current draw the output voltage can become "lumpy". If the device being powered is designed to be used with a regulated power supply, this ripple bleed through into the circuitry. This may cause erratic operation of digital equipment or audible hum and noise in audio equipment.
Regulated power supplies fall into two categories.
Older linear units still contain a simple transformer, rectifier and capacitor arrangement, but also contain a regulator to eliminate the issues outlined above. Depending on the type of regulator employed in the design, the power supply may generate a fair bit of heat when supplying high current.
Newer units are of the switchmode type. In general these are much more efficient and therefore run much cooler than the equivalent linear types. They are also often available with a universal input voltage range. (usually 90V - 260V, 47Hz - 63Hz)
How do you know if a particular power supply is regulated or not? Firstly, it may say "regulated" on the item or packaging! If not, there will be other clues. If it's a plugpack (wall wart) and is very light weight or has a "universal input" (85V - 260V AC) , the odds are that it is a switchmode type. (regulated by design) If it's an older linear type (heavier), then test the output voltage with no load. If the output voltage is very close to the stated (label) voltage, then it's almost certain that it's a regulated design. If the output voltage is more than a few percent higher or lower than the label voltage, then it's an unregulated design.
So, back to the question first posed. If the device you want to power states an acceptable DC input voltage range (10V - 16V for example), an unregulated power supply may be fine. On the other hand, some devices (often 5V ones) require that the input voltage always be within a few percent. You may need to seek guidance from the device manufacturer in some cases.