Warning -- Some wall warts are so horrendously bad at providing a clean and guarenteed voltage. Thats why the devices they connect to will have a voltage regulator inside to ensure that the voltage doesn't peak incorrectly.

The older "heavy" ones are simply a 1:10 (12 V), 1:20 (6V), etc... transformer winding with a simple diode providing half wave rectifiction to DC power. Any slight change in incoming voltage directly affects output voltage, and any change in amp draw affects the voltage provided as well. These will definitely want to be fed through some smoother circuitry. In the case of 5V, a couple capacitors and LM7805 regulator transistor added to the wart will provide a clean 5V output. There are regulators available in the 3.3V range too. Then you don't have to fear of slight spikes taking out the connected items.

The newer ones that weigh almost nothing, half the size or slender, are actually cheap switch-mode transformers inside. A high frequency tiny transformer, some driving transistors and other circuitry to convert the power. They may be better able to provide a clean(er) source of power; but at the cost of "cheap import" quality components.