You might also need one of those Scotch Guard brand scrubber sponges that has a normal sponge on one side and a more abrasive surface on the other side (it's not steel wool and won't scratch plates), and you might need steel wool (SOS or Brillo) if you have food caked onto pots and pans (but don't use steel wool on nonstick or cast-iron pans). I don't use normal dish soap on wine glasses, opting instead for a particular wine glass detergent I prefer, but that's me being picky.
We use
Scotch-Brite Dobies, which are sponges wrapped in coarse-textured woven plastic that is useful for scouring. We also have
Bar Keepers Friend, a powdered abrasive cleaner, under the sink. I personally don't use it often, but it is the only thing that actually restores an even shine to the bottom of the stainless steel skillet I use for pasta sauces, omelette fillings, etc. (Dawn dish soap will lift all the food residue but leave the bottom looking streaky and dull).
I realize not all will have the counter space to spare, but we typically use an area next to the sink for staging dirty dishes, including ones that are soaking with a few drops of dish soap in warm water to release food stains.
My large frying pan that I use for making tacos. Anything to do with tacos, really, including the bowl I put the meat in afterwards and the Tupperware container I put the leftover meat in. The meat and sauce leave far too much grease for me to clean; if I tried, I'd ruin my sponge to the point where I'd need to throw it out, and the item still would not be clean. Even the brush I use to prewash these items needs to go into the dishwasher to be cleaned, and it's only several weeks after I'm done with a taco cycle that it starts to look clean again.
We often presoak with hot water and dish soap to clean cookware and food storage containers that have held oily or greasy food. The dish soap will lift most of the fatty residue and a scouring pad (Dobie or similar), also dosed with soap, will take care of the rest.
The drip tray for my George Foreman grill that I use for hamburgers. Like the tacos, I can't clean the fat, even after draining most of it into another container.
Again, dish soap is your friend. We don't have a George Foreman grill, but we have similar issues with our chicken roasting pan, which we use once every two weeks in the summer.
My glasses; for some reason, they tend not to get clean very well by handwashing. Fortunately, since it's just me and I only drink water at home, they don't need to be constantly washed.
Glasses can be challenging. We occasionally soak ours in neat vinegar to lift mineral stains, and simply drinking beer out of them will do the same.
There's also the issue of volume. I can only hand wash so much at once due to limited drying room. Plus the soap only lasts so long before the sponge has mostly water. I'm probably not doing it right (I put some soap on either my spatula or a plate depending on whether I'm using the dishwasher for most things or not; I always have to handwash some because the frying pan I use for eggs is non-stick and I need both it and the spatula everyday anyways; and then I just re-use the now soapy sponge until I'm done), but that's what happens when you teach yourself with no reference.
My go-to is a Dobie and I dose it with dish soap at the start, re-dosing as needed when I see it is not lifting oil anymore (e.g., visible fingerprints or oily film after rinsing).
I don't actually wash non-stick pans--I just use a paper towel on the non-stick surface to lift most of the canola oil I use for eggs, and wet-wipe the bottom and handle.
