Andy wrote:

You should just go with the cheap white LED's. They give off a
more natural light vs those blue ones.

Andy comments:

There's other stuff in the blue LED lamp that makes it work only
on the half cycle (there's maybe 50%), and a couple current
limiting resistors also....

Here's a page showing a few circuits for powering one or two LED's
directly from 120 Vac power line.

http://www.qsl.net/yo5ofh/hobby%20ci...d_circuits.htm

Plus lots of other LED circuits that remind me when I was building stuff
like this on a breadboard back in junior high.

But yes, it seems common to use a capacitor and resistor in series, as
well as as diode across the LED:

==========
Using a capacitor to drop the voltage and a small resistor to limit the
inrush current. Since the capacitor must pass current in both
directions, a small diode is connected in parallel with the LED to
provide a path for the negative half cycle and also to limit the reverse
voltage across the LED. A second LED with the polarity reversed may be
subsituted for the diode, or a tri-color LED could be used which would
appear orange with alternating current.

The circuit is fairly efficient and draws only about a half watt from
the line. The resistor value (1K / half watt) was chosen to limit the
worst case inrush current to about 150 mA which will drop to less than
30 mA in a millisecond as the capacitor charges. This appears be a safe
value, I have switched the circuit on and off many times without damage
to the LED.

The 0.47 uF capacitor has a reactance of 5600 ohms at 60 cycles so the
LED current is about 20 mA half wave, or 10 mA average. A larger
capacitor will increase the current and a smaller one will reduce it.
The capacitor must be a non-polarized type with a voltage rating of 200
volts or more.
===========