Cheeses: The classic trio includes one hard (like a Cheddar or solid sheep's-milk variety), one soft (goat or Brie), and one pungent (blue), but you can choose whatever you prefer.
Nuts and Seeds: Nut brittles (find them in the candy aisle) are fantastic accompaniments. The salty-sweet combination goes especially well with hard cheeses. Nuts like walnuts and almonds are traditionally used in pairings; for a new take, try pumpkin seeds, toasted sesame seeds, and pine nuts.
Fruits: So many fruits go well with cheese: fresh berries for mild ones, cherries for blue, pineapple for alpine cheeses such as Gruyere, and apples, pears, apricots, and cranberries for almost all. Fruit can be raw, roasted, poached, stewed, dried, or in a jam. Try cooking down a bag of frozen berries until they thicken, then serve with a spoon in a small bowl. Curds, including rhubarb, lemon, and passion fruit, are great, as are strips of dried citrus zests, like orange, lemon, or grapefruit. For cured meats, add chunks of melon or apple slices.
Pickles: Their acidity helps balance the fat in cheese and meat. Carrots, crunchy okra, or green beans are all good with stinky, pungent, or hard cheeses (they may overwhelm mild ones). Cornichons pair especially well with charcuterie.
Spices/Herbs: You can coat a soft cheese with herbs or nuts—cut it into wedges, then press sesame or poppy seeds, basil, paprika, or peppercorns into one side. You can also use cumin, porcini mushroom powder, or a blend of powdered citrus zest and red pepper flakes.
Breads, crackers, vegetables, and spreads...