I'm pretty strict about not using plastic or paper bags. If I've forgotten to bring my reusable bags with me to work and need to go to the store, I will either buy another reusable bag ("green bags" for $1 at most groceries), or I just postpone my shopping trip til the next day. I don't have a car so I usually end up making at least 3-4 trips to the grocery store each week, just getting stuff I need - only as much as I can carry at any given time. Also, if it's not groceries, I carry a large canvas bag around with me every day anyway (hides my purse and allows me to have 1-2 books with me at all times!) so I just stick random things in it. Get some strange looks from cashiers, but I'd rather be weird than contribute more to pollution! ;D
I try to use reusable, but when that isn't really feasible, all of us (roommates and I) reuse plastic shopping bags as trash bags, or for any other number of things. Saves on buying trash bags.
As for what I buy..? It really varies seasonally. I keep stock of some basics; flour, spices, herbs, but other than that, it depends. Right now, I'm on a sandwich and fruit kick. So lots of fruit, cucumbers, hummus, and semolina bread. Mmm.
I used to walk to the local LIDL at least twice a week. I hate shopping (agoraphobia will do that) so now that DH is retired he drives me to a larger, better one a little farther away once a week and we do the shopping together. I do take my own denim shopping bags, made out of old jeans. DH seldom uses the car at all anymore so he says it keeps it running to take it out that once.
I too have had to train the local veg shop: No, I don't want a plastic bag! No, I don't care if the lemons and the onions get mixed together! Put it in my denim bag!! I also will give the pharmacist back those stupid, tiny plastic bags they give you with a box of aspirin or toothpaste, and tuck it in my purse instead.
When I had a cat, I used the tiny plastic bags for daily litterbox "triage". I don't have one anymore so I make a point of not accepting tiny bags.
I've noticed that more and more shops I go to now encourage shoppers to buy and use reusable bags. This is true of IKEA (home furnishing store) and Wegman's (foodstore).
OOPS I clicked plastic bag when I ALWAYS use my own bags!!! AHHH change my vote please :D