I’ve got some bad news about Boards of Canada, though.
Damn! That is some list! I didn’t know Canada had that many people. 
I’ll try to wing it without putting much thought into it:
Rush, Neil Young, Metric, Sarah Mac, bunch of others, but too lazy to look them up.
I have two albums by Dan Mangan that I still listen to.
Whew, I withdrew my post because due to the weird way these are being ordered I wasn’t sure that the bottom list was the list you only had one album by, but now it’s all good.
From most number to least number (because that’s how I’m used to ordering):
Odds
Sloan (They both have the same number of albums,3, on my digital media, but I have 2 unripped Odds CDs.)
Our Lady Peace (I only have their best of and only listen to the first 4 tracks: I dislike the rest of the tracks but those 4 songs are the best grunge-based songs ever.)
Guess Who
Rush (I actually like Rush more and have more stuff by them but haven’t ripped any of it. I’ve bought only 2 Guess Who songs but they’re in digital format.)
CSNY (which counts even less than rush because they’re less Canadian and I only have them on cassette which is less digital.)
RUSH
Pat Travers
Barenaked Ladies
Cowboy Junkies
Saga
Triumph
The Guess Who
S.N.F.U.
Frontline Assembly (Noise Unit/Cyberaktif/Delerium/Intermix)
Skinny Puppy (ohGr/Cyberaktif/The Tear Garden/Download)
Neil Young
The Tragically Hip
Les Georges Leningrad
Men Without Hats
13 Engines
Duchess Says
Koban
Sloan
Thrive
Natalie MacMaster (~5 tracks)
The Guess Who (~2 tracks)
There might be more, but I’m not going to sit down and go through the entire list of my digital music, many of which I have only one track by, to look and see if they’re Canadian. The numbers above are just from memory.
One of those “one-trackers” I’ve discovered is Canadian by reading this thread, and had to Google the name to make sure if it was actually the person I was thinking of:
Loreena McKennitt
If you count physical media, add Rush, but I have not converted any of my Rush albums to digital tracks.
In descending order, with totals from iTunes:
New Pornographers (90)
(tie) Arcade Fire, Tegan and Sara (75)
Metric (64)
Feist (49)
Grimes (33)
Stars (26)
(tie) Carly Rae Jepsen, Sarah McLachlan (23)
Purity Ring (21)
(tie) Alvvays, Rush (19)
I’ve got 8 other Canadian albums (10 if you count CSNY and Divine Fits) and a couple of singles. This all adds up to 611 tracks out of 9,668.
My biggest surprise was that I owned Moving Pictures. The exact tie for second also surprised me.
I forgot Milks and Rectangles. A few years ago I found a lot of bands by Googling random phrases and seeing if there were bands of that name. That name was taken from a sample from Frontier Psychiatrist by the Avalanches.
Other bands along those lines I’ve discovered are The TV Sound (Duran Duran reference), Matt Fisher and the Telephone Junkies (Elvis Costello), The Cocktail Revisionists (Jets to Brazil), and Dear Ambellina (Coheed and Cambria) but none of them are Canadian afaik.
Canadian Club
Crown Royal
Seagram’s
oops, misread thread title as Canadian BRands.
- Oscar Peterson
- Neil Young
- Glenn Gould
- Joni Mitchell
- Rush
- Leonard Cohen
- Canadian Brass
- Natalie MacMaster
- Barenaked Ladies
- Gordon Lightfoot
Bumped because…well, so I can show off my love for Oscar Peterson!
I had a lot more success when I looked at the Canadian solo artists page. I have four Bryan Adams albums, two Avril Lavigne albums, a Justin Bieber album, an Alanis Morissette album, and a Sarah McLachlan album. Only Canadian band for which I own an album is Our Lady Peace.
Rush- everything they did
Triumph- everything they did
The Band
Robbie Robertson- solo albums
Neil Young
Rik Emmet- solo albums
Jeff Healey Band
Barenaked Ladies
Bruce Cockburn
More that I will listen to on the radio but I don’t own.
Bruce Cockburn
(was surprised to realize he beat out Neil Young on my hard drive – just saw him do a high energy show with some blistering guitar work)
Neil Young (solo, and with Crazy Horse… does CSNY count?)
Leonard Cohen
The Band
Robbie Robertson and Rick Danko, solo/other bands
Ron Sexsmith
Joni Mitchell
Gordon Lightfoot
Cowboy Junkies
*And artists I didn’t know were Canadian before this thread (I mean, they seemed so normal…):
*
Stars
Tegan and Sara
Arcade Fire
Feist
Bachman-Turner Overdrive
The Guess Who (Live at the Paramount , and Greatest Hits)
The Band (Greatest Hits)
Neil Young
Damn, I forgot the Canadian Brass. They’re quite good.
I like to brag that I’ve seen all my favourite Canadian bands in concert, but the one I have the most songs of in my phone right now is The Arkells, who I have not seen yet. I did meet the singer and the bass player at the airport in Vancouver (they were on their way to Toronto for the MuchMusic Video Awards) so I count that a little bit.