What one ingredient can’t you live without? For me, it’s onions. I can’t think of one savory dish that I make that doesn’t contain onions. And sometimes LOTS of them. And sometimes more than one type of onion.
Probably water. 
Okay, serious answer: you’re asking two very different questions. I have potatoes with many meals, but I don’t think there’s one ingredient without which I couldn’t live. Just the other day I substituted the white bit of a leek for an onion in Sauce Diane and it worked very well.
Yeah, thinking about it a bit, I very often start out with the onion family in the pan.
ETA: re: water. I rarely use water; usually my liquid is a juice, broth, wine, etc. They may all contain water, but just plain water is something I seldom use.
Another vote for onions. Soups, crock pot meals, sautéed alone or with mushrooms, battered and fried - pretty much anyway but raw for me.
Tony Chachere’s Creole Seasoning.
Mirepoix Would be a better answer than onion, but it is more than one ingredient. Just to split some hair in your soup.
Vegemite!
By volume it would be onions, but by occurrences garlic would be tied with onions. I don’t know of anything I cook that includes onions without also including garlic.
I was going to say onions, but I almost use onions & garlic together. More onions, though, only because you generally need a smaller amount of garlic.
I also thought ‘butter’ but I also use olive oil, canola, or sometimes shortening so that’s probably not right unless you lump them together as ‘fat.’
Olive oil.
If mirepoix is on the table, why not go further with a battuto?
Consider my horizons broadened!
Whichever variation of pasta happens to be open. But then, if pasta wasn’t available I’d just do the same with rice.
Butter.
I have 3 ingredients that are tied for first, depending on how “used most” is measured.
Tomato sauce, onion powder, and garlic powder. I like my real onions, too, but I use a lot of the dried stuff in spaghetti sauce and chili.
Cinnamon, because every day it goes in my coffee and on my oatmeal. I also add it to cookies, brownies, bread pudding, hot chocolate and some chicken dishes.
I’m definitely an onion guy, but I tend to be onions or garlic, not both, for a good number of dishes, especially Italian ones.
Onions are kind of an easy answer. Old-time cookbooks used to advise that if you weren’t sure what you wanted to make for supper, you could always start by sauteing some onions.
On garlic, meanwhile, my personal view is that if it makes sense to ask the question “should this have garlic in it?”, then the answer is yes. But that’s also kind of an easy one.
The most distinctive ingredient I use (that is, one that I use a lot more than most people) is crushed black olives. They add a nice zing to almost any dish.
Ayup.
I will say that I am making a (coconut) birthday cake for my wife tonight; so while I will surely use the old staples of butter, flour, sugar and eggs, I will probably leave out the onions and garlic.