Condiments include ketchup, mustard, mayonnaise, hot sauce, soy sauce, salad dressings, jams, and other sauces and spreads that accompany food. Their storage needs vary widely - many are shelf-stable while sealed but should be refrigerated once opened, while some (like honey) keep best at room temperature and others (like natural nut butters) need the fridge from the start.
A good rule of thumb: high-acid, high-sugar, or high-salt condiments resist spoilage and often only need refrigeration for quality rather than safety. Always check the label, and when in doubt, refrigerate after opening. Check each item's guide for specifics.