I have designed sevreral simple AC-powered LED projects, using a capacitor as the series input voltage-dropper (think of it as an AC resistor). To calculate the reactance of a capacitor, the formula is Xc = 1/(2*PI*F*C), units are in Ohms, Hz and Farads.
To simplify things greatly, this works out to
1,000,000 / 377 X C (in uF). So a 1 uF cap
would have 1,000,000 / 377 or approximately
2620 Ohms effective "resistance" at 60 Hz,
and 1,000,000 / 314 = 3180 Ohms at 50 Hz.
(Figures approximate, I don't have my calculator handy)
A varistor should be used across the LED circuitry to protect from any transients or spikes on the line.
As an example, I use a 2.2 uF, 250 VAC cap, and a 47 Volt Varistor, and a full wave rectifier bridge to power a 36 White LED light, using one of the B.G. Micro IR Illuminator boards. I use 330 Ohm resistors,
(one in each series string of 9 White LEDs, and a 50 to 100 uF, 50 VDC cap to smooth out the DC and eliminate the "flicker". I have had one of these units running for well over 2 years and it is still going strong.
Disclaimer: If you are not really thoroughly familiar with working with AC-powered circuitry, don't try this, one little mistake can be lethal, so have a friend who is good with electronics do the work for you.
/ed brown