Savvy hounds never toss out shrimp shells after peeling the shrimp for cooking. Instead, freeze the shells (and any heads) until you have enough to make shrimp stock.
Shrimp stock turns up the flavor in shrimpy New Orleans–style dishes such as gumbo, shrimp Creole, and shrimp étouffée. BigSal is a fan of Paul Prudhomme's Seafood Dirty Rice, which is made with shrimp stock.
Shrimp stock is a great base for seafood soups. Add diced canned tomatoes, onion, celery, carrot, potato, seasonings, and fresh or canned clams, says greygarious, and "Voilà! Manhattan clam chowder." janetms383 uses shrimp stock to make tom yum, Thai coconut curry soup, and ozinboz recommends Penang hokkien mee, a slightly spicy Malaysian noodle soup.
Use shrimp stock to cook grain dishes, such as pilaf or risotto, when you want deep seafood flavor. scubadoo97 cooks grits in it when he makes shrimp and grits.
Discuss: What to do with shrimp stock