i rock the three-bag system for trips to the coop. probably half the people i know from the coop recognize my giant green backpack first and me second. i think the carts are a pain both on the subway and once i get home, where i have to shoulder all my bags in order to get them, me, and the cart up the stairs anyway. like limone, i now have superstrength, and i'm so good at estimating the weight of a cart of groceries that i could probably make a killing as a carny. keepin' that dream alive in my back pocket.
my grocery bags are buried in a box somewhere that i haven't unpacked and carts look to be no better than carrying bags so it's been plastic. the downside is that i now have a growing ball of plastic in my apt.
i have yet to be asked 'paper or plastic' so does one need to show some leg in order to get paper?
i kid..sort of
Whole Foods does paper by default (I honestly don't even know if they offer plastic), and I think TJ's does paper, too. Honestly though I've just gotten used to carrying foldable cloth bags in my gigantic purse at all times. Flip and Tumble makes sturdy ones that hold up to 35 pounds and they live up to their claim. I've had mine for over a year now and have filled it to the brim without any issue.
I don't even do a backpack - I just ruin my back by carrying shoulder bags over both shoulders. But if you want to go the backpack route, you could always get a Chrome messenger bag or backpack. They're sturdy as all hell and hold a lot of stuff.
IN MY DAY I CARRIED 40 POUNDS OF GROCERIES HOME A MILE AWAY FROM TRADER JOES. (I'm not even kidding.)