2 Transformerless Power Supply

This is one way of converting your AC supply to DC without using any transformer. This power supply uses a capacitor that provides an AC impedance that limits current and voltage to your load. This power supply is a cheap way of providing power  low current DC devices. A typical circuit is shown below.
The key part of the circuit is the capacitor C1 which provides an equivalent impedance of :

Capacitor impedance formula

The four diodes D rectify the AC to DC and capacitor C2  and zener Z1 smoothens and regulates the voltage  that is delivered to your load.

Transformerless power supply schematic

12V version power supply materials:

R1- 560k 1/4W
C1- 220nF suppression capacitor
D- 1N4007 diode or similar
C2 -22uf  25V electrolytic capacitor
Z1- 12v zener 1W

Refer to the schematic above for the abbreviations. The circuit is good only for  12V low power DC devices that can consume only around 15mA current.

Danger:
We cant deny that this power supply is much cheaper and much smaller compared to any transformer based power supply of same power rating. But we must keep on mind that this type of AC to DC converter has no main source isolation thus touching any part can cause electrocution. I don't recommend of building this power supply if you don't or have  little background in electrical engineering. Build this power supply at your own risk.