Whammy Bar
The whammy bar can be used to drop (and raise on some bridges) the pitch of all 6 strings. It allows a number of techniques to enhance one's playing.
Contents
Dive-Bomb
The classic whammy bar technique is called a dive-bomb. It involves simply pressing the bar down further and further until the strings becomes slack. Any notes that were sustaining when the dive-bomb begins will drop further and further in pitch until they turn into low frequency noise.
This technique is simple: just keep pushing on the bar! The only thing to watch out for is that open strings will start ringing as you add more slack. I like to mute those strings with my left-hand before starting the dive. However, in some cases, that open-string ringing may be a desirable part of the effect, especially once the strings are completely slacked.
Slide to Nowhere
This technique uses contrary motion by sliding up the frets on one or more strings as you push down on the whammy bar. The trick is to time them so that they are increasing and decreasing the pitch at the same rate, so that it doesn't sound like the pitch is changing. Once you've gone pretty far (~7 frets), you can reverse directions by sliding down while decreasing pressure on the bar to continue the effect. Or you can release the bar quickly, so the pitch rises very quickly, like you stored all the energy from the slide and are releasing it all at once.
Vibrato
The whammy bar makes an excellent means to get vibrato. It's probably the best or only way to do so for chords and the least noisy way to do so for notes that are sustaining until they completely decay. See here.
Eastern Instruments
One of the characteristic sounds of Eastern stringed instruments is the the downward pitch shift during the attack of a note. This can be simulated by pulling up on the whammy bar while picking a note but instantly releasing the bar. It may not be necessary to pick the string, but instead use a hammer-on, or pull-off/slide from an existing note. Sliding down into a note while using this technique can take it a step further.
Synth
A common way to embellish a synth sound is to pitch shift upwards, into the note. This can be simulated with bending, but often bending is too slow and limited in pitch to mimic some of the more noticeable synth effects. So instead we use the whammy bar, depressing it before plucking the desired note, then quickly releasing it afterward/during. With the strings slacked by depressing the bar, it's often unnecessary to pick the string at all - a hammer-on works just as well, freeing your right hand to focus exclusively on timing the bar.
Flutter
On a floating bridge, one performs a flutter by quickly hitting/pushing the bar and sliding off of it, causing the bridge to snap back towards its resting position. Because the floating bridge relies purely on counter-balancing tensions to find its resting point, the momentum of the snap-back carries it past neutral position, where it then changes directions. It flutters around the neutral point before returning to rest. It's basically like a super-fast, diminishing vibrato.
To get a feel for the technique, position the bar so it is pointing towards the nut. Push the bar down with your ring and pinky fingers from your picking hand to lower the pitch of all the strings but don't wrap your fingers around and grip the bar. Now move your entire right hand towards the nut while maintainting pressure against the bar - your fingers will start to slide towards the end of the bar. Keep moving your hand, allowing your fingers to slide off the tip of the bar. With nothing to maintain pressure, the bar pops back towards neutral, but flutters before getting there.
One can perform a flutter by using the bar initially in either direction. In other words, you can point the bar towards the back strap pin or the opposite direction of the nut. Now if you push on the bar, it will raise the pitch of the strings. But if you slide-off and let it snap back to neutral, it will still flutter the same as when done the opposite direction.
Most flutters are done while the note is sustaining, almost like a secondary accent. For example, if the same note is played consecutively on the 1 and 2 beat of a measure, the performer may pluck the first beat then use a flutter on the 2nd beat.