Probably one of the most common and cheap power supply circuits used to power low current applications directly from AC. You would have used these for sure at your homes in LED night lamps, fan regulators(Maybe a future post when I get time) or any of the cheap gadgets that plugin directly to your mains AC supply. The elegant part of the circuit is that it removes the need for a bulky transformer and can be built with very few components.
The pictures are of LED night lamp which plugs into mains directly. It consists of a higher wattage in-rush current limiting resistor(R1, during turn ON of the device, so as to not let a large current through initially), and a capacitor(C1) in series with the mains(Instead of another resistor). The capacitor is designed to give impedance without losing power as heat at 50Hz. The resistor (R2) is a large wattage resistor which acts as a bleeder resistance to discharge the capacitor when the device is OFF(To avoid shocks if you touch it). The overall circuit has a poor Power factor but has low active power consumption. This is basically all because of the capacitive dropper circuit section.
The rest of the circuit is a four-diode bridge rectifier to convert to DC, and an electrolytic capacitor(C2) to smooth the DC at the output. This is really not needed if you really wanted to skimp on parts. LEDs will work fine on AC(you may see flickering though sometimes).