Jesus this is long. I probably made spelling/gramatical errors because I wrote this post as quickly as possible without proofreading.
Johannes Ockeghem - Anything. He was the master of canon - moreso than Bach even. See Un Hermita Solus which was perhaps the most complex canon he ever wrote. Renaissance music at it's finest. (note: for people who have studied 16th century species counterpoint, his music sounds somewhat unorthodox as it was written before those conventions had been established).
J.S. Bach - Musical Offering, Die Kunst Der Fugue, Well-Tempered Clavier, St. Matthew's Passion, B minor Mass, Sonatas and Partitas for solo violin, Goldberg Variations, Solo cello sonatas, Brandenburg Concerti, organ works, Cantatas. Needs no introduction. Musical Offering has probably the finest tonal canon writing ever (Ockeghem wrote in a modal idiom). My favorite Brandenburg is the 4th for the amazing fugue. Also, he wrote a number of pieces that have a great deal of quirky, "rule-breaking" dissonance in them. Glenn Gould is my favorite interpreter of his keyboard music.
Mozart - Like Bach, he wrote so much good music that it's hard to pick just a few pieces. Both of his G minor symphonies stand out to me. He played with form in very interesting ways and expanded the kinds of intervals that were acceptable for use in melody writing greatly. I like the second of his Eb major horn concerti a whole lot. This piece contains beautiful melody writing for the soloist and a lot of quirky gestures from the orchestra. The quintet for winds and piano (he considered it his finest work - me too maybe). The "Dissonant" string quartet - the beginning has 30 seconds of music that sounds like it came from Schoenberg. Cosi fan Tutti - great aria. Don Giovanni - too much cool shit to explain here. Great piano sonatas too.
Beethoven - More great piano music (op 109 and 111). Symphonies (these should be familiar). 13th string quartet in Bb major + Grosse Fugue: my favorite music of his - especially the Grosse Fugue. That piece could have been written yesterday and people would still say it's groundbreaking.
Mahler - Das Lied von der Erde is an interesting work of his that combines both of his favorite writing styles - symphonies and song cycles. All of his symphonies have much to offer - from their greatly expanded tonal harmonic vocabulary to their innovative orchestrations. My favorites are 2, 7, and 8. In many ways, the arch late-Romantic composer.
Brahms - Symphonies 3 and 4 (particularly 3). In some ways conservative (because he was the late Romantic composer most attached to the music of the classical period), he was nonetheless an unsurpassed innovator. Probably my favorite romantic composer with his sound and intricate structures. His music is full of beautiful melodies and, harmonically, it moves around to very remote places incredibly fast and smoothly. It's not dissonant in the same way as Wagner or Mahler and as such it doesn't sound as jarring to someone with an untrained ear but if you can recognize the modulations, his music can really catch you off guard. That's probably what I like best about Brahms - his music moves around to so many different places but so smoothly. He often writes very long melodies in his symphonies that move through a variety of key areas and change instruments as they go along - with the instrumental timbre getting farther and farther removed from the original instrument(s) as the line progresses. Another notable aspect of his style is it's rhythmic compexity (including various subdivisions of the beat such as quintuplets, etc and odd large-scale rhythms) Clarinet quintet and violin concerto are great too.
Charles Ives - Concord Sonata, 114 songs, 4th symphony. Perhaps the ultimate musical experimenter and writer of Americana par excellance. His list of innovations would be too long to list here. Just get the 4th Symphony and hear what the hype is all about for yourself.
Arnold Schoenberg - A composer who overcame extreme artistic and personal adversity (mst dramatically when the Nazis came to power as he was Jewish and a composer of "degenerate" music). Probably the most importat composer of the 20th century started off by taking the music of the late romantic farther than anyone else and finally breaking with tonality in 1907 (I think) with his op. 11 piano pieces. Later, he wrote his op23 which was the first fully-formed twelve-tone piece (Ives wrote music with twelve-tone rows long before Schoenberg). His Woodwind Quintet, 3rd and 4th string quartets (both are amazing - especially the 4th), String Trio, Violin concerto, all utilize the immensely important twelve-tone technique of running a row against a transposed inversion such that the first 6 notes of the first row combined with the first 6 notes of the second row all add up to an aggregate of all twelve pitch classes. This technique allows for the music to progress in partially-ordered harmonic units of all twelve notes affording a flexibility of orderings on the musical surface. I consider that to be his single most important contribution to music. Great technical innovations in twelve-tone serialism used towards writing music that I consider powerfully emotionally resonant (or the man who killed classical music depending on how you look at it). Also, his violin concerto most likely contains the first blast beat.
Stravinsky - Les Noces, Sacre du Printemps, Petruschka, Threni, Symphony of Psalms (more metal than metal!), Huxley variations, Requiem Canticles, Movements for Orchestra. He started out using polytonal techniques, influeces of Eastern European and Russian folk music and a jarringly individual rhythmic style to write the works he's best known for but later on in life decided to take up twelve-tone composition and arrived at a technique of rotating and transposing rows (wholly different from anything in Schoenberg or any other twelve-tone composer of the time) that, combined with his signature rhythmic style, led to him wrting some of the most unprecedented twelve-tone music in the literature. Great vocal writing and idiosyncratic uses of instrumental color. Huxley Variations is probably my favorite work of his.
Ruth Crawford-Seeger - I don't know too much about her other than that her string quartet is one of the best pieces of American music ever written. She, like Charles Ives, was sort of an oddball composer who made innovations in a number of different musical areas including rhythmic technique (use of different length cycles), and serial music (what criteria she used for the transformation of her musical materials). The only other piece of hers that I know is a short, difficult oboe work that I played on guitar once. I was fortunate enough to see the quartet once and that was mind-blowing so I think it should be included here. Pete Seeger's mother.
Olivier Messaien - Used birdsongs, rhythmic cycles of varying lengths, influences of Indian and Indonesian music, and symmetric scales to write his own very individual style of music. Quator pour la fin du temps, written while he was incarcerated in a German prison camp, is probably his most important work and, in many ways, serves as a catalog of his compositional techniques. There are some demanding, virtuostic passages that, because of their aggressive articulations, rhythms, contours, and melodic/harmonic materials, should be mandatory study for all tech metal musicians.
Elliot Carter - his primary technical innovations lie in areas of rhythm. Early in his career, he developed the technique that erroneously became known as "metrical modulation". It should really be called tempo modulation. It works by changing a subdivision of the beat of a measure in one tempo and having it equal a different subdivision in the next measure in a different time signature thus creating a new tempo. (i.e. quintuplet 16ths in one measure = 8th note triplets in the next measure). The best early example of this technique is his Sonata for Cello and Piano (beautiful and virtuostic!). He's since taken the technique so far that it's more difficult to hear it and recognize what's going on. His other main rhythmic innovation is the "structural polyrhythm" where a huge polyrhythm (ridiculous ratios like 67:59:35 cycling against each other too slow for a listener to hear) spanning an entire piece or a large section of it, is composed out over a large scale with tempo changes or large attacks happening at specific points with other music happening in between these spots. Usually one instrument or ensemble articulates a cycle of the polyrhythm. He also likes using the structural polyrhythm technique and metrical modulation to have ensembles or instruments (or different voices on a single instrument) playing at different tempi at once. Double Concerto for harpsichord, piano and two orchestras is a good example of this kind of writing, as is the 3rd quartet, Night Fantasies for solo piano, 5th quartet, Clarinet concerto, etc. His pitch language, while thoroughly atonal is not twelve-tone. Rather, he uses a harmonic framework that he composes out intuitively as he pleases. Seek out Ursula Oppens' piano interpretations of his music for unmatched virtuosity and sensitive interpretations.
Milton Babbitt - before Pierre Boulez's famous "Structures" for two pianos which was widely regarded as the first application of serial principles to areas of music other than pitch, Milton Babbitt wrote three compositions for piano which were actually the first example of this style of writing (and FAR more musical than the Boulez). Since then he's been exploring the possibilities inherent in Schoenberg's twelve-tone system and has taken serial music farther than anyone else. His main innovations are in the use of combinatorial math to generalize on Schoenberg's combining of row forms. He devised what's come to be known as the all-partition array which is a pre-compositional construct using many rows running against each other and taking bits and pieces from different rows to create aggregates in all possible ways using each one once. He's after the maximal variety that serialism offers and applies it to all aspects of his music. He wants to make his music, "as much as it can be" rather than "as little as one can get away with" which is what led him to come up with all of his incredibly complex constructs. While the individual licks in his music maybe aren't always going at warp speed (although they definitely do sometimes), the speed at which his musical structures progress is probably beyond that of any other composer. Every aspect of his music conveys a new purely musical (as opposed to programmatic, or emotional, etc) meaning - from large scale formal gestures down to intervals. The complexity of his music (and his use of math to achieve that complexity) has made him one of the most maligned of composers today which is somewhat ironic considering that his music is, if you can wrap your ear around it, very pretty and light sounding in general. He also has the unfair reputation as being an austere elitist (due to the complexity of his compositions and theoretical writings as well as the extreme virtuosity needed to play his music) when his music is really full of humor and puns. A few of my favorites from him are All-Set for jazz ensemble, Partitions and Post-Partitions for solo piano, Canonical Form for piano, The Head of the Bed for soprano, clarinet, cello, violin and flute, Whirled Series for alto sax and piano (probably my favorite piece of music ever!), Reflections for piano and synthesized tape, 6th string quartet, Sextets and The Joy of More Sextets (the cover of the LP looks like the cover of The Joy of Sex!), and Soli e Duettini for flute and guitar. From purely a listening perspective, I find his music quirky and beautiful sounding. My favorite composer hands down.
Brian Ferneyhough - English composer who writes music that's unplayable - only approximations by the best performers are possible - although still rather attractive sounding. He, like Babbitt, is much more interested in notes and rhythms than in creating textural sound masses like the eastern Europen composers. An important area of interest for him is microtonality but performed on conventional instruments. While Babbitt expects people to play his barely playable music accurately, Ferneyhough expects people to fuck his unplayable music up in interesting ways! His music is very philosophical in nature (dealing particularly with questions of identity) and can often be heard as an immensely intricate dialogue between the different elements that make up music (melody, harmony, sound, gesture, rhythm, etc). His 3rd and 4th string quartets, Terrain (which is a sort of chamber concerto for violin), La Chute d'Icare are favorites and, for all their complexity, I get a sort of romantic vibe from them.
artofthestates.org is a great resource for hearing pieces by contemporary American composers for free. (By the way, the version of Babbitt's "Partitions" on there isn't so good - the performer sounds heavy-handed and he rushes the piece! Robert Taub's or Alan Feinberg's versions are much better.)
Other notables are Berio's sequenzas for solo instruments and Chemins pieces (sequenzas with orchestral accompaniments) and some of Xenakis' music, Schubert's lieder, Webern's op 27 piano variations and his two Cantatas, Boulez's explosante-fixe... for flute, midi-flute and orchestra (not a serial piece!). The list goes on and on...
