depends what you have in the cup. A cup is a measure of volume, but a gram is a measure of mass.
Here is a list to help you out.
Granulated sugar: 1 cup = 200 grams
Brown sugar: 1 cup, packed = 220 grams
Sifted white flour: 1 cup = 125 grams
White rice, uncooked: 1 cup = 185 grams
White rice, cooked: 1 cup = 175 grams
Butter: 1 cup = 227 grams
Almonds, slivered: 1 cup = 108 grams
Oil: 1 cup = 224 grams
Maple syrup: 1 cup = 322 grams
Milk, non-fat: 1 cup = 245 grams
Milk, sweetened condensed: 306 grams
Broccoli, flowerets: 1 cup = 71 grams
Raisins: 1 cup, packed = 165 grams
Milk, dry: 1 cup = 68 grams
Yogurt: 1 cup = 245 grams
Water: 1 cup = 236 grams
Confectioners sugar: 1 C = 110 g
Cocoa: 1 C = 125 g