I got this question for last week's Ask the Blogger (remember, you can submit questions for next week's Ask the Blogger at firstname.lastname@example.org). It's a tough one, like asking whether I would choose my husband or my dog. I'm going to make the right choice, but it's going to be agonizing find a new home for my husband.
(Kidding! I'll be here all week. Don't forget to tip your waiters.)
At first blush, the choice is actually really easy: my Thermomix. I use it the most of any of my appliances, as it can do the job of mixer, blender, food processor, and scale, along with some things that none of them do, like cooking food right in the bowl.
But the questioner was clever, and directed me to specifically exclude the Thermomix, on the grounds that it is outrageously expensive and unlikely to become a standard household item in America. That makes the question a little bit harder.
So I cast my mind back to my pre-Thermomix kitchen, and what was on the counter. I have a rule about expensive gadgets: they have to sit on the counter, or in an easily accessible appliance garage. If you have to go to the basement or under the cabinets to get it out, you won't use it, and it's not worth the money. I do have specialty appliances that don't live on the counter: crockpot, griddler, waffle iron, pasta machine, and so forth. But the rule is that they have to cost under $100 and be fairly portable.
What lives on my counter all the time? Sous-vide machine, vacuum sealer, stand mixer, Thermomix (used to be a food processor), toaster oven, and stick blender. But while I use all of these appliances regularly, I wouldn't say they're all indispensable. The sous vide machine is fantastic, and I use it far more than I ever would have expected. But there are other ways of cooking meat. We could get along without it, though to be sure, you would have to pry my husband's whitened knuckles off the sides before you'd be able to take it away from us. Without the sous-vide, I definitely wouldn't cling to the vacuum sealer, though it does save us some money.
The toaster oven is great--convenient, fast, and keeps my kitchen from going to 800 degrees in the summer. But we don't eat *that* much toast, and anyway, in a pinch, you can make toast in the oven. (Yes, my little chickadees, it's true: toast was invented before toasters.)
I like my stick blender (which is technically on the wall, not the counter). But it's a convenience, not a necessity; you can replicate everything it does, somewhat tediously and messily, in a food processor, blender, or stand mixer.
You cannot make pesto in a stand mixer.
There's no ice cream attachment for my food processor.
My food processor makes perfect pie crust.
My stand mixer makes amazing cookies.
My biscuit recipe calls for a food processor.
My pound cake recipe requires a stand mixer.
Back and forth it goes. And the winner is . . . the stand mixer, by a hair.
The food processor makes a lot of dishes a lot easier. But I could conceivably do most of what I do in a food processor by hand. On the other hand, I don't see myself creaming butter and sugar by hand for 15 or 20 minutes in order to get the same consistency my stand mixer achieves in 5. I'm sure if I'd grown up on a 19th century farm, this would be as child's play. But I've missed my window for Popeye-sized forearms. And I've never had good results trying to make cake batter in a food processor, though all the companies swear you can do it.
Your mileage may vary, of course: for a non-baker, I'd say that a food processor is hands down the most useful. But really, what this exercise makes me realize is how very glad I am that I don't have to choose.