Cook spaghetti to desired doneness as directed on package. Drain.
Meanwhile, heat oven to 375°F. In large saucepan or Dutch oven, brown ground turkey with onion and garlic; drain if necessary. Stir in sugar, oregano, basil, salt, pepper, tomatoes, tomato paste and mushrooms. Bring to a boil. Reduce heat; cover and simmer 20 minutes, stirring occasionally. Remove from heat; stir in cooked spaghetti.
Place half of spaghetti mixture in ungreased 13x9-inch (3-quart) baking dish; sprinkle with mozzarella cheese. Top with remaining spaghetti mixture; sprinkle with Parmesan cheese.* Bake at 375°F. for 30 to 40 minutes or until bubbly.