Heat oil from anchovy fillets in heavy large deep skillet over medium-high heat.
Add sausage and break apart with spoon. Cook until beginning to brown and crisp, stirring sausage often, about 7-10 minutes.
Add anchovy fillets and garlic; stir 1 minute.
Add crushed tomatoes, pitted green olives, drained capers, smoked paprika, and dried oregano.
Simmer tomato sauce 5 minutes to blend flavors.
Season sauce to taste with salt and pepper.
Meanwhile, cook spaghetti in boiling salted water until just tender but still firm to bite.
Drain pasta; divide among plates. Top with sauce. Garnish with Parmesan cheese, if desired.
