I'm in agreement that a .47uF cap works well, but you still have to have some sort of resistor in series (1K or so), otherwise really short risetimes will blow the LEDs. I use resistors here because they are smaller than a 400V cap.

RE: Transformers - I needed to measure the "quality" of the AC line. I thought I would use a cheap transformer. The transformer would power both my PIC and provide the low-voltage isolated signal to the PICs A/D.
I realized that the peaks would be chopped off by the bridge rectifier as the voltage rose a diode drop higher than the main storage capacitor, so I put a 150 ohm resistor in series with the diode to "soften the blow". The
PIC didn't take much current, anyway, so the extra drop of the resistor wasn't a problem.
But I was mistaken! Even with the current limit, the waveform coming from the transformer was horribly distorted. I wound up using a (TAMURA brand) transformer that was about 6X as big (in current ability) than I needed, and one that had TWO separate secondaries. One secondary ran the PIC, and I used the other to measure the line. The "unloaded" secondary fed a bridge rectifier that had only a 680 ohm resistor as a load. That worked.