pekasus:
Chicago Dave - this is the first time I've seen a 0.22u cap in line with the LED. As I saw in the comments, this reduces current, but does it heat up a lot? Also, for a 120v line, I guess I would use a 250v cap instead of a 400v, correct?Thanks again for all your help!
Should've mentioned... those caps are "X2" caps, and are meant to be connected to 'mains' power. They're "special". 
And, you should be able to use a 250v (275v) cap for 120v line, but it shouldn't be an issue to use a cap rated for higher voltage than needed. -- 'Better safe than sorry!'
For the first image (w/ 2 diagrams) I uploaded, the LED will be 240v above earth if the active and neutral are swapped and this represents a shock of over 340v if anything is exposed. The power diode in the first diagram is designed to discharge the 0.22u during one half of the cycle so that the capacitor will charge during the other half-cycle and deliver energy to the LED. The 1k resistor limits the peak in-rush current when the circuit is first turned on and the mains happens to be at a peak.
As second diagram shows, two LEDs can be driven from the same circuit as one LED will be illuminated during the first half cycle and the other LED will be driven during the second half of the cycle. Second LED just replaces the normal "power diode" in first diagram.