I try, I really do, but my bins are always full. Frugality always has to be my number one priority, but this can produce extra 'food' for the bins.
For instance, I buy bottled water because the water in my area tastes dreadful, and believe it or not, buying 6 smaller bottles actually works out cheaper than buying one larger one. I re-use and upcycle many of these empty bottles (there's zillions of ideas on the www) but you can't recycle them all.
I buy a lot of food for my feline family, pouches mostly, sometimes tins. The pouches are also packed in boxes making double the packaging. I also recycle a lot of these boxes, my main use is for when I sell a fragile item on Ebay, they make good strong packing boxes.
Cat litter - I have three of those a week too, I cut out the inner strong brown paper lining, run a hot iron over it and store it for packing also, this saves me buying any more paper. I also use this for craft items.
Plastic bags, love 'em or hate 'em, they're everywhere. There has been talk for a long time about discontinuing them (the free ones that is) but it's not happened yet. This again is a double edged sword, because I reuse the bags in lots of different ways, mostly as bin liners, so that saves me having to buy them.
Margarine/yoghurt tubs and anything with a lid on always come in handy for storing sewing supplies and small items, also small leftover items of food, sauces etc., for the freezer, but they last forever and you can't keep them all.
Clean waste paper is shredded and used as packing, I also use it for my handmade papers.
There are many other examples, but there's always too much to recycle and it ends up in the bin.
I do my best ...