My kitchen isn't fully simplified by any means... But what made it a lot better was to rearrange all of the items so that they were near their point-of-use. All of the food prep items, like mixing bowls, measuring cups, pots and pans, etc, are in one lazy susan corner cabinet. All of the food storage items, such as leftover containers, aluminum foil, baggies, and such are in another. Plates, glasses, and cutlery are all near the dishwasher and sink. All of the spices, oils, and sauces are near the stove. Seems obvious, but I was much less organized for a while.
Another thing I did was to get glass leftover dishes. I think they're Anchor. They have rubbery plastic lids, but they're microwave safe and don't iscolor like plastic. I use them as serving dishes, then just pop on the lid and put what's left in the fridge. I can microwave the entire portion without worrying about leaching chemicals or melting.
Gadgets? I have a parmesan grater that you'd have to pry from my cold dead hands before I'd give it up! I LOVE fresh parmesan. Also a can opener, if you consider that a gadget. Other than that, I think I'm pretty gadget-less.
Appliances.... I have a toaster oven and microwave on the counter. A coffee pot in the cupboard. A single-serve blender, crock pot, rice cooker, food chopper, and a hand mixer down in the cabinets below. I could live without everything but the crock pot, mixer, and coffee pot. I'd have a rough time without the toaster oven, but I could use the oven in a pinch.
I don't have a ton of pots and pans. 3 pans, 4 pots, and a enameled cast iron dutch oven. I could get rid of the small size pan and medium sized pot and not miss them much. I do have a big canning kettle and a pressure cooker/canner, but those are going to be moving to the basement when DH builds my new shelves.
I have 8 place settings of dishes and 8 glasses. 12 place settings of flatware. We have family over for dinner about 6 times a year, so 8 is the minimum for us. I couldn't live with just 1 setting per person, even if we never had guests. We'd have to wash after every meal, and I'm just not that dedicated. I prefer one big sinkful every night. We have no paper plates, and we're going to be phasing out paper napkins. pretty soon.
I have quite a lot of pantry staples. We have food storage, so I always have a lot of the basics on-hand. We have a small dedicated pantry in the kitchen itself (the rest lives in the basement). I try to keep about two weeks to a month's worth in the kitchen. Then when I grocery shop, I just rotate it when I unpack the new food.
I'm interested in what others will say, since this is an area that I always seem to be working on!