My favorite Canadian band is The Guess Who. Sorry, Arcade Fire and the Tragically Hip. But most of my favorites show up on the original greatest hits album.
The Wikipedia explains the band moniker: “Quality Records credited the  single [Shakin’ All Over] only to “Guess Who?” in an attempt to build a mystique around the record… After Quality Records revealed the band to be Chad Allan & The Expressions, disc jockeys continued to announce the group as Guess Who?, effectively forcing the band to accept the new name.”
Sometime after Chad Allen left, the lineup I knew the best, and was most commercially successful, was Randy Bachman (guitar), Burton Cummings (vocals and keyboards), Jim Kale (bass), and Garry Peterson (drums). Bachman left in 1970 to eventually form Bachman-Turner Overdrive, and was replaced by guitarists Greg Leskiw and the late Kurt Winter.
Today the name The Guess Who is owned by Garry Peterson and James Kale.
“These Eyes” (Cummings, Bachman), #6 in 1969, their first single on their new label, RCA Victor — here or here
“Laughing” (Cummings, Bachman), #10 in 1969, and one of the very few singles I purchased as a teen – I was an LP kind of guy — here or here
“Undun” (Bachman) — #22 in 1969 as the B-side to “Laughing” – here or here
“No Time” (Cummings, Bachman), #5 in 1970 — here or here
“American Woman” (Cummings, Bachman, Peterson, Kale), #1 for three weeks in 1970, which they did NOT play at the Nixon White House — here or here or here (album version)
“No Sugar Tonight/New Mother Nature” (Cummings, Bachman) — “No Sugar Tonight” was the B-side of “American Woman” – here or here
“Hand Me Down World” (Winter), #17 in 1970 — here or here
“Bus Rider” (Winter), B-side of “Share the Land”, and my least favorite song on the album — here or here
“Share the Land” (Cummings), #10 in 1970 — here or here
“Do You Miss Me Darlin’?” (Cummings, Winter) — B-side of “Hang on to Your Life”, and probably the better choice for a single here or here
“Hang On to Your Life” (Cummings, Winter) — #43 in 1971; the single version does NOT have Psalm 22:14,15 at the end; I’ve put this version on a religious mixed tape – here or here
Also listen to The Guess Who – Anthology (2003)