A simple bridge rectifier and filter such as this device, will charge the cap to the peak of the voltage, 18 V in X 1.414 = 25.2 volts DC. Remember that AC is given in EMF or a DC equivalent, even your 120 volt wall outlet, since both halves of the cycles are there with no rectification, you have 120 X 2.828, or 340 volts peak to peak at the outlet. When you load this supply, assuming you feed it with 18VAC, it will drop to as low as 12 volts and be very ripply. A bridge rectifier with no filter will supply .707 time EMF volts, in this case 12 volts from 18VAC in. Of course a regulator will help with voltage stability, but if you load this unregulated supply and you get a usable voltage with acceptable ripple they work fine. You can also add more capacitance to smooth the DC more, but there is always a trade off based on just how much current you need, and whether you need it fairly pure for things like audio. Normally a good regulated supply with smooth DC out, requires an minimum 18 volt transformer to get smooth 12. Switching supplies are another animal altogether. An analog supply with linear regulator of say 12 volts at 5 amps is a fairly large thing, but as a switcher supply, 12V at 5 amps can be the size, and weight almost, of a pack of cigarettes.
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