Same thing with condiments as I have stated previously with spices, you can get away without almost anything on this list but having them will give you a sense of normalcy and make your storage food more palatable. I do feel strongly about having copious amounts of Lemon Juice because it is very important for canning and dehydrating on your own but everything else on this list can be made on your own or passed over if your not a fan.
Soy Sauce
Sweet and Sour Sauce
Gyoza Sauce
Lemon Juice
Ketchup
Mustard
Tabasco
Relish
A-1
BBQ Sauce
Non-Dairy Creamer
Sweet n Low (or Equal, we prefer Splenda around here though.)
Worcestershire Sauce
Dijon Mustard
Pancake Syrup (super east to make on your own)
Horseradish