This is easier than you think. Don't use the store bags for the cat litter, if you are just using them to pick out the poo. Use other discard bags, like bread bags, cereal, the small plastic bags you put fresh vegetables in, frozen veggie bags--and use the bigger store bags for the liners.
Mooch store bags from your non-granola friends and family. In exchange, give them a cloth bag and tell them to quit with the plastic, already.
I have been shocked, upon reflection, at how many bags I throw out that I got food or whatever in. Especially bread and cereal.

Hope that helps.

I have the same problem, but with paper bags. I always reused my paper grocery bags for lots of things, but mostly for taking out the newspapers for recycling, for storing my shredded paper and ripped-up cardboard for the compost pile, and for storing redeemables. Now I'm reduced to asking co-workers to bring me any paper bags they might have, because I have none in the house!

finnbiker has some good ideas, both in trying to use the other bags (I know lots of them are smaller, but you might be able to use them) and in asking other people for their used plastic grocery bags. It's really amazing how many people throw out those bags, unfortunately.

:)
Dee

Here, the daily newspaper is delivered in a plastic sleeve, just right for picking up kitty nuggets.

Wastebasket liners-I sometimes use dog food bags (I have big dogs, buy the 18 lb bags).

Pick up "Grounds for the Garden" at Starbucks;
if they give them to you in the silver bags, use those for smaller jobs.

if they give you the big trash bags, well, there you go.

Being a gardener, I cruise alleys & curbs on the nights before trash pick-up, especially in neighborhoods that have big trees;
it's just astonishing-
people rake up their leaves & bag them & set them in the alley for me.

Once the leaves go into the garden or the compost heap, I often have a perfectly useable trash bag.

If the top is knotted too tightly to untie, rip open the bottom seam & dump out the leaves or grounds, & re-tie the top so that there's no gap & use the tied end for the bottom of your "new" trash bag.

Oh, sylvia, you just reminded me of something - I don't know why I didn't think of it on my own as I just emptied one the other day.

Anyway, Matt, if you use bagged topsoil, manure, mulch, peat moss, potting soil, etc., you might have some resources. I open bags of these things carefully near the top, and I save them when they are emptied for garbage bags in the garage and around the yard, etc. It might be a bit different to use them in the house, but perhaps a quick rinse for some of them may do the trick. You might not want to use the manure bags in the house, but mulch and potting mix bags might not be so bad.

These are great ideas! You're right, there's no shortage of plastic elsewhere...

Dee, for the newspapers, I had the same problem with not having any paper bags any more. Maybe something like the link below? You thread some twine, drop in the papers and then tie 'em up and bring 'em to the curb.

You know, it's funny, I used to use the plastic bags from the newspaper for the kitty litter, but (a) out here they only use them when it's raining and (b)I decided the newspaper was distracting me from my kids and filling up the recycling, so I canceled it!

Here is a link that might be useful: Paper recycling bin

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More on Starbucks:

The "silver bullet" bags are great for temporary flower pots.

Poke drainage holes in the bottom, & since they're pretty deep, you might want to trim off some of the top of the bag.

excellent for moving plants around, as they take up less space than rigid plastic pots.