I think we need to focus on a Mastercard or VISA to use for everyday shopping. Is CIBC Aerogold VISA Infinite the best non-Amex card for earning Aeroplan miles in Canada? Are there Mastercard or VISA products for OneWorld (e.g. AA) or SkyTeam (e.g. DL)?
Non-Amex cards of interest, with details for regular spending (as opposed to bonus/churning):
CIBC Aventura/Aerogold - $120 annual fee, 1 AP/$, 1.5x for gas/groceries/drug stores
RBC Avion - $120 annual fee, 1 Avion/$, 1.25x on travel, transferable to AA/BA/CX 1:1 (with 1:1.5 BA and 1:1.25 AA promos sometimes)
CapOne Delta - $120 annual fee, 1 DL/$
TD American Airlines - $120 annual fee, 1 AA/$
Also, a great candidate for regular spending (particularly for me, I have more miles than I can use right now) is the CapOne Aspire World - $120 fee, $350 "travel dollars" sign-up bonus, $100 "travel dollars" annual bonus, 2% back in "travel dollars". Mind you, "travel dollars" are tiered and only guaranteed 2% for redemptions against travel charges at exactly $150, $350 or >=$600, and no partial redemptions.
EDIT: RBC Avion has a current offer for first year free, 20K Avion after first spend.