The first circuit shows a single LED using 110VAC. I used this circuit to detect if voltaje is present at the AC outlet. A reversed diode is needed because the LED have a limit on reversed voltage. The second circuit labeled as "Night light" is basically the same circuit but it uses two LEDs. I use it to create a soft light in my room and walls to avoid accidents when I walk around the house during the night.
By the way: I don't walk sleeping. Also, it can be used to know if an unknown voltage is AC or DC. AC voltages will lit both LEDs. The third circuit is used in my power supply so I can detect when I need another fuse. The last circuit, the "LED light" is an experiment to illuminate my room with LEDs instead of fluorescent light or light bulbs. It works fine as a 13 watts fluorescent light but the light emitted is not even. Anyway, it is perfect to save electricity.