Tate - I confess I missed your post first time round, but that's a really good summary of most of the main points about serialism. I'd add an extra point: although 'serialism' and '12-note' (or '12-tone' or 'dodecaphonic') are usually used synonymously, they're not quite. 12-note music is always serial, but serial music is not always 12-note - it's perfectly possible to apply the techniques of serialism to collections of notes ('tone rows') to fewer than (or more than) 12 notes. A lot of Stravinsky's serial music works with rows of fewer than 12 notes, for example.
But that's a minor point that only sticklers like myself really get worked up about.
A brief listening list, emphasising the range of styles that use the serial technique:
Schoenberg: Variations for Orchestra
Webern: Concerto for Eight Instruments
Berg: Violin Concerto
Stravinsky: Requiem Canticles
Messiaen: Mode de valeurs et d'intensites (Quatre etudes de rhythme)
Babbitt: Three Compositions for Piano
Boulez: Le marteau sans maitre
Nono: Il canto sospeso
Stockhausen: Kreuzspiel
There are tons more than this. One of the common fallacies about serialism is that it was a relatively homogenous movement in music; in fact it was incredibly diverse. Many composers only really flirted with serialism (Messiaen, Ligeti, Gorecki), and more either weren't terribly comfortable with it (Stravinsky?) or quickly evolved their methods far beyond the strictures of serial technique (Boulez, Nono, Stockhausen). And some, like Berg, are remembered as serial composers when in fact it makes up only a small proportion of their output.
But for all this, and for the continuing controversy over its apparently elevated place in musical history (see Kyle Gann's blog periodically for his polemics on this subject), serialism was and remains a potent source of inspiration for many composers.