Inevitably there's going to be some kind of subjectivity to any answer. I'll take your word "innovative" to mean "unprecedented". These are my suggestions:

The anonymous author and composer of Musica Enchiriadis, a 9th century treatise devoted partly to polyphony. It didn't actually invent polyphony (strictly, the simultaneous sounding of more than one note; more accurately, two or more musical lines or melodies that are complementary but also independent in both pitch and rhythm), but it attempted to codify its practices. The polyphonic principle underlies practically all subsequent Western music except monophony (i.e. a single unaccompanied melody), which proportionally speaking is fairly thin on the ground.
The composers of the late 14th century avant garde, a style known as the Ars Subtilior ("most subtle art"). This is a highly mannered style whose exponents went far beyond contemporary practice in terms of pitch and rhythmic complexity, using extreme chromaticism and combining different time signatures. Composers include Solage, the music of whose piece Fumeux fume par fumee ("The smoky one smokes through smoke") can only be described as being as bizarre as the text.
Gesualdo (1566-1613). An Italian prince who murdered his wife, her lover and (possibly) their son when he caught them in flagrante dilecto. He remarried, by all accounts quite happily. Then he wrote his last two books of madrigals, which are way off the scale of what was normal for the time. They're chromatic to the nth degree, a degree that presages Wagner.
Edgard Varese (1883-1965). The first composer to write a piece consisting entirely of unpitched sounds: Ionization, for 13 percussionists. This was a contradiction of the most basic constituent of Western music since Gregorian chant: determinate pitch. It paved the way for the electronic music of a few decades later.
Charles Ives (1874-1954). He pioneered many techniques such as polytonality, polyrhythm, tone clusters, aleatoric music (in which the performer rather than the composer determines some of the piece's elements) and quarter tones (intervals smaller than the semitones you see on a keyboard).

Doubtless others would chip in with such luminaries as Claudio Monteverdi (1567-1643), the first composer to break with the Renaissance polyphonic musical traditions and to launch what is now known as the Baroque period; Beethoven (1770-1827), who realised the potential for the personally expressive and the titanic in music; and my own beloved Wagner (1813-1883), who revolutionised both opera and the orchestra and - in the view of many - pushed music to the boundaries of tonality, making Schoenberg (1874-1954) inevitable. Speaking of which - Schoenberg, Stravinsky (1882-1971) and Debussy (1862-1918) each played their part in breaking some boundaries. Schoenberg finally ditched the major-minor tonal system that had been the norm since about 1650; Stravinsky turned the previous Romantic century around completely; and Debussy was one of the first to bend the tonal system beyond breaking point, leaving only its remnants in his work. However, all of the above could be seen as relying on their predecessors rather than being truly independent of them.

For my money, however, the most innovatory composer of all time is Franz Liszt (1811-1886). No, not the Liszt of the Liebestraum, but the Liszt of the late piano music. He pioneered techniques that were decades ahead of his time. He was the first to write a piece of whole tone music (one based on a scale consisting purely of tones, not a mixture of tones and semitones as are the major and minor scales of tonality). Much of this late stuff is atonal - in fact, one of the pieces is his Bagatelle without Tonality. His dissonances are simply inexplicable in terms of any conventional tonal treatment; they include a tone cluster, a la Ives and Cowell. Liszt himself wrote on the cover of one of these experimental pieces, the Czardas Macabre (which consists of a string of parallel 5ths, a progression forbidden for about half a millennium), "Is it allowed to write such stuff, or listen to it?" As an index of how revolutionary this late music was, iconoclasts and progressives one and two generations later - namely, Debussy and Bartok respectively - were gobsmacked when they discovered this stuff. Very dark music, most of it, and thus very much an acquired taste. Enjoy!

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