Hellobee Boards

I LOVE LOVE LOVE these! They are collapsible, with rigid sides and bottoms. I have regular ones, and cooler bag style ones with a lid.

I've only ever seen them at Hy-Vee though

https://www.hy-vee.com/grocery/PD24287935/Collapsible-Shopping-Box-Purple-with-Polka-Dots

found a 3 pack on Amazon

https://smile.amazon.com/Earthwise-Reusable-Shopping-COLLAPSIBLE-Reinforced/dp/B0711K553G/ref=mp_s_a_1_2?ie=UTF8&qid=1536376573&sr=8-2-spons&pi=AC_SX236_SY340_FMwebp_QL65&keywords=collapsible+shopping+bags&psc=1

And this is the cooler bag version

https://smile.amazon.com/Earthwise-Insulated-Reusable-Shopping-REINFORCED/dp/B06W9NYGSV/ref=mp_s_a_1_8?ie=UTF8&qid=1536376573&sr=8-8&pi=AC_SX236_SY340_FMwebp_QL65&keywords=collapsible+shopping+bags&dpPl=1&dpID=51YNSZLNUkL&ref=plSrch

ETA:

I collapse all but 1, and put them in the one bag; they fit on the bottom of the cart or I use a giant caribeaner clip from my stroller to clip the handle of the bag to the handle of the cart

We have the blue reusable bags that were at Costco years ago. They can hold a ton. I haven't seen them lately though.

For grocery shopping I have ones really similar to the earthwise collapsible ones - they are great and I love that they stay upright in my trunk.

For general day to day running errands I LOVE my baggu standard size bags. They fold up small enough that I keep 2 or 3 in my purse at all times. They can hold up to 50 pounds and the handles are long enough to go over my shoulder.

My favorites are the insulated bags from trader joe’s I have one for each car, and I store the thinner bags inside the insulated bag. Mine last for years, and they stay upright in the car when full. I hate the ones that are always falling over.

I bought a CarryWell set over a year ago and I still love it and it’s held up beautifully.
The 10-pc set has 6 bags that are bigger than the ones I used to use - despite not having a plastic bottom they’re well structured. It also has a cooler bag, and a couple produce mesh bags. If you wanted you could turn the bag caddy into a wine bottle carrier, or just use it for a few bottles when you’ve taken some bags out for a shopping trip. Side pockets for extra bags or coupons or whatever are also nice.
10 Piece Reusable Shopping Bag & Produce Bags Organizer Tote Bag Set | 6x Reusable Grocery Bags with handles, 2x Mesh Produce Bags, Insulated Freezer Bag, 6-Bottle Wine Carrier| Convenient/Heavy Duty https://www.amazon.com/dp/B01L4QMHW2/ref=cm_sw_r_cp_api_QbiLBbGHJ19H5

@meadow: they're amazing! Only style of reusable bag I'll buy now! Glad you like them