When music is your quest, then both sound and silence are are your friends.

"...music is composed of only 2 things: sound and silence. The silence is the delay between the sounds. It is often overseen but it is as important as the sound... To be able produce a silence of the desired length requires a good time perception... I find it harder to learn than sound as it is more void. Silence would an absence, sound more an presence and the interaction between the two is music. The simplicity is only apparent, even people who play djembe for more than 20 years still improve their sound and silence."

Source : http://off.net/~jme/djembe_tut.html
This reciprocation between sound and silence is obvious in some kinds of music (Jazz, Trip Hop) and not so obvious in others (Death Metal, Pop). It might even be missing sometimes (Punk, and I say this is in a derogatory sense), or overused (4'33" by John Cage). It also depends a lot upon the instrument in case (percussion and bass place a huge emphasis on rests and syncopation). Even within the same song, one instrument might use silence relative it itself, while other sounds might be continiously droning in the background (the bassline in Who knew - Eminem, Dazed and confused - Led Zeppelin).

quick dirty example : use your mouth to boom at the roughly indicated intervals (try not to do this in inappropriate situations, you know)

boom  boom  boom  boom (most techno and trance)
bom boooooom      boom (swing feel)
boooooooooooooooooooom (the bass is killing me)
boom  boom             (Clap back - Ja rule)
boooom       boom boom (left as an exercise for the discerning student)
you can also combine variable length boom's and insert groovy silence between them, as Limp bizkit does in Nookie
boom boom boo boom   b boom boom  boom boom
note: I know this is lame. /msg me if anyone has a better idea to explain this.
see also - how to post multimedia content on e2.

As you see, we used the same single sound to produce various musical works by simply varying the proportion and duration of silence and sound. The possibilities are endless.

The first and foremost example of someone who uses silence to great effect is Pink floyd. Shine on you crazy diamond is basically silence interspersed with sound. It takes a tortoiseque 4:24 minutes for the introductory solo to finish - thats about the time that most songs themselves last. The riffs in Wish you were here are so embedded in silence that every note becomes something to be treasured. And ofcourse, how could I forget Echoes - it isn't everyday that you get to hear a 23:41 minute song.

Jimi hendrix is another person who uses silence to great effect. Infact, his style in this area remains unique to this day. Both his vocals and his guitar playing are in a timezone of their own, and there is no way you can classify his rhythm, no way you can tell when the next note is coming. Seemingly disconnected notes and out_of_key vocals jump out of the blue (or rather, purple) haze; it's only later that you realise that everything makes sense in its own weird way. join the disconnected parts and you'll get to see why this guy wasn't in from this universe.

Dub musicians have mastered silence - dub basslines seem to have a life of their own. ditto for breakbeat music, the drum solo at the later part of Influx by DJ shadow being a good case in point.

The breaks in trance work similarly- by inserting silence before the big break, the feeling of the anticipation is heightened. A scientific explanation you might ask for, but I offer none. maybe what this silence does is make the ear more receptive, exactly in the same way as being alone draws attention.

try not to confuse silence with slow tempo or low volume. Music can be fast and loud yet use silence to a great effect (Poor Twisted me - Metallica, Piggy - Nine Inch Nails, Cocain - Eric Clapton)

Now guess what - Clint Eastwood Western movies. You just have to hear these movies to experience the unbelievable tension and expectancy that the backing soundtrack (rather the lack of it) creates. Typical scene sequence : silence. horsewoofs, protagonist enters the dusty main street. stops. silence. thud, he jumps off from the horse. silence. creek, door of the city inn opens and the bad guy comes out. silence. both guys reach for their guns. silence. silence. silence. wind blows. birds chirp. silence. silence. silence. BAM, thank you maam.

now for a ignorable rant...
electronic music is not bad. I love electronic music. but what people seem to be forgetting in this digital world is that time is not discrete. Fruity loops is the most killer electronic music application I've seen, yet like every other music software, it has a fundamental flaw - quantization. dividing time into interval won't work, simply because time cannot be divided into intervals. and that is why...

...analog rules.