The Beatles.

Ok, maybe not.

How about The Band? They were Bob Dylan's backing band and then went on to have one of the best selling live albums of all time, as well as a live concert film directe by Francis Ford Coppola!

Here are some more:

Colin James
Cowboy Junkies
Sarah Mclachlan
Wide Mouth Mason (somewhat interesting trio with an Oriental bassist!)
Kim Mitchell/Max Webster
The Tragically Hip
Big Wreck

That's all I can think of off the top of my head!