I use open plastic bins for things in bags: rice, beans, lentils, etc. After a nasty infestation of pantry moths, I put all those things in separate zipper bags. I do the same for flour and cornmeal type products unless they are in a closed canister. That way, if anything came from the store containing bugs, at least it will be contained! I use the bins for things like boxes of tea too - we always seem to have a ton of that and I have no idea where it comes from! I have a separate bin for dog stuff - biscuits, chew sticks, etc.
I also use a couple of those lazy Susan type spinners - one is a single level and 1 is a two-tier unit. Those are good for small things as long as you don't spin too fast!
I have a large plastic bucket with a latching lid for dog food - it's easier than opening the whole bag. I keep a scoop or a plastic tupperware-type container inside for scooping - great use for those containers that have a missing lid.
I find that those old fashioned spice racks you can still find in thrift shops and yard sales are great for the small things - spices you don't use often, food coloring and other baking supplies (cupcake paper liners or almond extract for example, that you don't need regularly), any packets used like dressing or gravy things, bouillon cubes, birthday candles, etc. That can be attached to the wall or to the inside of the door.
Clear boxes or even see-through shoeboxes are great for stuff that doesn't stack well, or smaller items like tuna cans that stack but might tilt if they go through the wire.
I keep baking stuff together, soups together, and then I put beans together and pasta products together, with tomato puree in between because I use it for the products on either side. I also try not to get too carried away with stock-up sales, but if I bring home new stuff by mistake, I put it in the back and move the older product forward.
Office store organizers can be helpful - for example, the book racks can be good at holding up boxes of cereal or crackers (except the giant ones) so they don't tip over on the wire shelves. I also use them for cookbooks, especially the thin ones that tip over. They're good for storing small trays and trivets too.
This isn't exactly what you asked for, but I also use the insides of cabinet doors for posting things for quick reference - a listing of offices in the Town Hall, school contact numbers, emergency instructions, business cards I might want but haven't put into my phone yet, take out menus, etc. Gets them off the counter or the front of the fridge.
I've also seen people use an old dish drainer for plastic leftover containers (stacked) and then the lids go in the slots where you would put the plates, 2 or 3 to a slot.
If you use bins, definitely go to the trouble of labeling them so you can see at a glance where stuff goes. But too many bins take up space of their own, so be judicious in their use.