I learned these while working in food service, but after blowing my brother's mind when I made my own cocktail sauce instead of buying it, I realized that some people may still be buying these instead of making their own. I always have this stuff around the house and it makes a lot more sense to mix up my own whenever I need it.
Cocktail Sauce: mix ketchup and grated horseradish until it looks/tastes right
Tartar Sauce: Mix mayonnaise and pickle relish until it looks/tastes right
Horseradish Sauce (serve with rare roast beef): Mix sour cream and horseradish sauce until (you guessed it!) it looks/tastes right
Those are the ones I do the most often. It's not culinary wizardry, but maybe you're like my brother- it makes sense but you never thought to do it yourself!