When you say sauce, do you mean only as something to dip or place on top of food? I don’t think I would survive without mayo, but not that I really use it as a sauce (besides spreading it on hamburgers), but because of the stuff I eat it in.
Italian dressing
Another vote for horseradish.
I’d have to say BBQ sauce but that might be cheating since there’s a billion different kinds but that’s what I love about it.
Right now my current obsession is this:
pineapple hot sauce. It’s so sweet and spicy it’s perfect. They don’t sell it locally, that I could find, so I bought about 8 bottles a couple of months ago to stock up.
I’m torn between ketchup and catsup.
Vodka.
Oh, you mean actual sauce.
Another vote for Sweet Chili sauce.
And breath mints afterwards, because that stuff is loaded with garlic! LONG after the sweetness and the heat is gone, the garlic lives forever!
~VOW
(second place is mole–LOVE that stuff!)
BBQ, there are so many different kinds and so many utilities.
scoff
Mole is what BBQ wants to be when it grows up.
~VOW
Pesto, if its a sauce, otherwise Sriracha.
What kind of mole? There’s about a gazillion different kinds, and I assume we only get to pick one… (Same with BBQ sauce. I don’t think it’d be fair to pick it out as a general category, because under BBQ you have sauces based on tomatoes, mustard, cider vinegar, and even mayonnaise.)
I, for one, salute your devotion to the scientific method. Thank you for reporting back with your results.
I prefer tomato sauce, but for me it would be Tabasco.
Pesto.
I came in here to say this, and I’m a little startled that more people haven’t. Maybe I’m misunderstanding the OP and they’re asking specifically about a “sauce” as in “sauce you add to a prepared dish for extra flavoring” and not “something called a sauce that you use in dressing or preparing a dish”?
Because if I have to go through life trying to cook without bechamel sauce, tomato sauce, mayonnaise, beurre blanc, pesto and all their relatives, I’ll be damned if I’ll sacrifice soy sauce as well for something as inessential as ketchup or triple ginger sauce.
(And that’s assuming I can still sneak in what some Anglophone culinary traditions call “salad sauces” by insisting that their name is “salad dressings”.)
Yep. Or caramel… it’s a sauce too, right? 
Béchamel. One of the mother sauces. In the South, we call it gravy. Oh sure, bicker and point how wrong I am.
It’s milk, flour and fat. It is the foundation of a cuisine that makes us fat and happy.
Hollandaise is pretty awesome.
Definitely soy. I’ll miss fish sauce and tomato sauce, but must have soy.
Hot Chilli.