This page discusses circuits that deal with 120VAC. Most of these circuits use triacs, silicon controlled recitifiers (SCR), diode, and diacs. Remember even though these may seem neat, please do not attempt any of this on your own unless you have experience with high voltage work.

The Silicon Controlled Rectifier or SCR is a very useful circuit component that is similar to a diode except for it has a gate. It is essentially a diode with a switch to turn it on and off. So when the gate is at a low voltage the SCR is off. Eventually if the gate voltage is increased it will turn on the SCR and current will flow from Anode to Cathode. This would seem useful for DC except for once the SCR latches on the current it is carrying must be cut before it will turn off. So AC signal could be controlled through this device except for the fact that it only allows through the positive portion of the wave. This fact will be discussed when looking at the circuits.
Here are some more thinks with information:
App Note
SCR info
The above is the shimmer circuit as it is refered to as. What is meant by shimmer is that it will cause the lights to clash from half intensity to full intensity. This flash is the shimmer. First, it is important to note than an SCR is being used. This gives some insight into the reason for the half intensity flash. This is because an SCR can only let the positive wave to pass thus the negative wave is conducted through D3 and thus the light is always halfway on. D1 then only allows the positive wave through to the SCR. In the off state the capcitor charges through R2. Then once a proper voltage is reached the gate gets triggered through the R3,R4, and R5 network. The pot R4 changes the rate of flash. The higher the resistance the more voltage needed to trigger and thus a slower flash. Finally, R1 and D2 are important to the discharging of the capacitor. Once the capacitor charges and the SCR triggers the capacitor can discharge through R2 and R1. If R1 is removed then after the initial flash the light stays on because the capacitor cannot discharge fast enough. The diode is important to ensure that R1 only takes part in the discharging and not the charging of the capacitor. This circuit was tested on a christmas tree and worked quite nicely.
This circuit is a complementary fader which means that the intensity of the two bulbs are opposite. The basic idea is SCR1 is the main SCR which gets controlled by an enternal trigger mechanism. In my case I just used pots equivalent to 1.2 MΩ. As SCR1 turns on more the current increases and more of the voltage drops across the light bulb and less across the SCR. This means that as the intensity increases the voltage at the anode of SCR1 and gate of SCR2 decreases thus turning off SCR2. When SCR1 is off you have the full voltage on the anode of SCR1 and thus SCR2 is fully on. The resistors are for biasing of the gates to work properly. The full wave rectifier is important as SCRs can only handle the positive wave so they rectify the signal so you have a full waveform to work with. This removes the half power situation of the shimmer circuit and will be seen again n the flasher circuit.
This circuit is nothing more than a modified version of the shimmer circuit shown earlier. The two difference are the addition of a full wave rectifier and removal of D3. The full wave rectifier turns a sine wave into the absolute value of sine and thus there is no negative portion and D3 can be removed. This means that the light is no longer partially on for part of the time and instead the light flashes on and off.

The diac is a circuit component that is not often learned or heard about. It is in a way like a back to back zener diode. The reason for this is that it has a breakdown voltage much like that of a zener. Once that breakdown voltage is reached it allows current to flow. Unlike a zener which has a different forward turn on and reverse breakdown voltage a diac has the same breakdown voltage in each direction and thus is often seen in AC circuits. It does have one important use which will be seen later.
Alternative Symbol: 
As can be seen from the alternative symbol a Triac is actually nothing more than two back to back SCRs. The importance of this is that now unlike the SCR it can conduct in both directions, this makes it very desirable for use with AC as it controls both positive and negative portions of the wave. Besides this it behaves much like an SCR. Below is some more information and some circuits using triacs.
Some more information on Triacs:
App Note
The Triac
Triac Info
This circuit is very useful for being able to remotely control 120VAC lines using low voltage DC source. This is useful if you want to control a light or other equipment with a computer or microcontroller. It replaces a mechanical relay and provides a cheaper alternative to more expensive solid state relays.
The macroscopic operation is rather straight forward. There are two main components in the circuit which are the opto-coupler (labeled MOC3020,23) and the triac itself. The opto-coupler provides isolation for the controller and safety incase the triac were to fail. So by applying a voltage to the left side the led in the opto-coupler will turn on. This in turn will allow current to flow from terminal 1 to the gate through the opto-coupler. This will then turn on the triac and allow current to flow from terminal 1 through terminal 2 thus turning on the load. It is important to note the size of the 180Ω resistor. This resistor was choosen because of the 1A peak max current of the opto-coupler. (See App Note for more information on how these choose the correct resistor size and about snubber circuits.) Then when you turn off the opto-coupler the triac will turn off once the next zero-crossing is reached, thus you have a solid state relay.
There are several things to consider when building this circuit. One is the value of Rin so that you meet the opto-coupler latching requirements but don't over current the LED. Also, as previously mentioned the value of the 180Ω resistor is important. The triac must also always have the gate triggered from terminal 1. If you flip the triac over it will stop working. Finally, remember 120VAC can kill you so be extremely careful and make sure you know what you are doing if you make this circuit.
This circuit is the basic cheap light dimmer that you will find in a home. It works by chopping up the waveform. The triac is only turned on for part of the wave and thus you get the lower intensity.
Voltage across the triac.
Now that you have seen the diagram and heard about the basic operation let's investigate what actually happens. We start off with the triac off and thus the light off. The capacitor charges through the resistor. Eventually a sufficiently high voltage is reached to trigger the diac to act and then current flows to the gate and turns on the triac and the light turns on. This is why the second half of the waveform is zero in the above picture. When the triac is on there is virtually no voltage drop across the triac and all the voltage drop is across the light since it is on. The resistor changes the RC time constant and effects the brightness. The more resistance the slower the capacitor charges and thus the dimmer the light.
NOTE: The values in the diagram are ones I chose, there are more, possibly better values to use, and they depend on the triac you are using.