For classical music I'm not sure how much argument could be put forward for anybody but Arnold Schönberg. His 12-tone/serialist method of composition dominated much of the mid-to-late 20th century art music world. You need only look at the Darmstadt school [led by Schönberg student Anton Webern] to see how pervasive this influence was. Even much of what has become the most popular forms of contemporary classical - the minimalism of Reich and Glass, the holy minimalism of Pärt, Tavener and Vasks and the neo-romantic works of Rautavaara, Górecki, Copland and Barber - arose largely as reactionary movements in the wake of serialist essentialism.
In the metal world I would put forth Slayer. During their peak period of 1984-1988 they laid down what has become, essentially, the extreme metal riffset. Some of their contemporaries became more commercially successful/popular, but who else could lay claim to such a pervasive influence across thrash, death and black metal? They are the bedrock - probably even more so than a band like Black Sabbath - of what contemporary metal has mutated into.
In terms of popular/rock music as a whole it would seem that it could only be The Beatles, right? I can't claim to be any sort of expert on their music - in fact I've never heard an entire album of their's - but surely they were trailblazers in writing/performing their own music, the popularity of the album as the primary format for consuming music, and for incorporating aspects of the then avantgarde [sound collage, Hindustani classical, etc.]. Not to mention their impact on culture at large; they are probably the most all-encompassing musical entity of all time. Everybody knows who they are. Even people who aren't interested, like myself.