I'm gonna have to go with
RUSH as the quintessential Canadian band.
Just like the nation the band just keeps on ticking, they've been around seemingly forever but never really in anyone's face. 44 years and still going strong is quite an achievement for any band, let alone one of their technical caliber. From humble beginnings they made attempts at success and rather than crumble when their label put pressure for that possibility for success to start paying back commercial dividends they strengthened their resolve and forced the industry to respect their position with their landmark 2112 album. Their styles are almost as varied as the cultures and people who populate the great white north (can't really think of any hip-hop experiments from the group though).
Virtuosos in their own rights and well recognized by their peers and fellow musicians the individual members of the band come across as very laid back and down to earth. No haughty attitudes and airs of superiority, they let their music be the star of its show rather than forcing their egos. It's like how Canada will forever be in the shadow of the USA but we've got a nicer reputation, not based on boastful claims, but from how people perceive our actions and society.
The other thing that really makes it feel Canadian to me is the proggy-psychedelicness for lack of a better term. Even in big cities there's not that much to do in comparison to an equally populated American city, and I think a major factor in that is the Winter. Our Winters are long and harsh, they limit the outward opportunities, and if you happen to be a snowbound musician it's the best time to beef up your chops and develop your own style, really though what else is there to do? I think that forced natural solitude in their formative years reflects itself well within the introspective metaphysical lyrics that dominates the majority of their work.
We're an innovative nation, we struggled to colonize a new world, we stepped up when our motherland called for help, we continue to strive for a better tomorrow, not just for ourselves but for everyone because we all deserve it. RUSH's musical career really encapsulates that, their innovation, their drive, their resolve, their hope for a better future. It's all there in their music.