Depending on the specific recipe, Greek yogurt, cream cheese, skim milk thickened with corn starch, or tofu thinned with soy milk can replace heavy cream. For vegans, coconut cream or cashews blended with liquid work well.
The Cooking Light website provides a heavy cream substitute recipe for soups. To make it, boil 2 cups unsalted chicken broth with 1/2 cup uncooked instant brown rice. Cover the pot, reduce the heat and simmer the mixture for 25 minutes. Remove the pot from the heat and leave it untouched for five minutes. Blend the mixture with 1 cup low-fat milk until smooth.