One of the most used sauces in United States in my experience, from side dishes to a principal component in salads, is Mayonnaise.
Usually when there is a salad on the table there is also oil, vinegar, salt and pepper to season it.
Here is one recipe for our friend the vegetarian. It is the base of any preparation in an industrial or domestic kitchen, and is another way to not waste vegetables or vegetables peelings.
I was working with a Chef that studied and worked in France. One time, I asked him why he added chicken stock to all the preparations and his answer actually made a lot of sense.