I’m redoing my kitchen shortly so I’ve been thinking about this quite a bit. (The redoing is borderline-crisis; the appliances are so old they’re avocado, and neither the dishwasher nor the oven works. I’m left with an energy-sucking fridge and a cooktop.)
Necessity:
The coffee maker. I recently indulged and bought a Krups Grinder-and-maker, which took only three months to go Kaputt. Thankfully, I’d saved my almost 10-year-old Braun, which still works great. Simple is Beautiful.
The microwave (how’d you make that micro symbol?). I generally cook a lot and reheat, so it’s a Joy and Wonder.
The dishwasher. Even though I live alone, I really miss it.
The KitchenAid Mixer. It was my mom’s, so there’s some sentimental value, too. Might replace it with a Bosch mixer/blender combo.
Non-appliance doohickeys: My cast-iron skillet. My knives. I use the 10" monster for large vegetables, the 8", which is curved nicely, for mincing, my Henkels boning knife for everything but boning (flexible blades are great), and then a 3" Global for paring. The Global knives (i only have the one) are stunning, wicked-sharp. Gradually I’ll replace the other knives. Oh, I also have a cheap bread knife.
Odd, little things I love: a “cream cheese spreader” that’s great for mayo on sandwiches. A little glass lump you throw into a pot of water - it rattles when the pot boils so I don’t need a kettle. My Le Creuset heat-resistent spatulas! (They’re amazing, and the extra expense is worth it - they withstand 500 deg. and still like new.) (And I recommend Le Creuset over other brands.)
Convenience
The nonstick cookware.
The bread-baker-toaster-oven. Could live without it, but why?
The electric skillet. Use this one all the time.
The (better) coffee grinder, purchased when the Krups Kaputted.
The (cheaper) coffee grinder, now used for herbs and spices (all eleven of 'em!)
The electric griddle. Great for breakfast when there’s a crowd, like every weekend at the beach house.
The Cuisinart. Don’t use it that often, but there are a few things that make it A Nice Thing to Have.
Coolness
My grandmother’s Toastmaster waffle iron. It was a wedding present to her in 1934, still works.
Other
I don’t use the blender much, either. It’s nice for the rare shake, but I don’t have those that often, especially since the dishwasher’s broken and I hate washing the damn thing by hand.
Now, here’s the kicker: All of the above coexist peacefully in a 45 square foot kitchen, along with a complete, 1950-era “everyday” service for 8 (including 20 serving pieces), about two dozen cookbooks, and, at the moment, some poison-resistant mice. (They’re eating the glue traps!!!)