Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
While the pasta cooks, heat the olive oil in a large skillet over medium heat.
Add the minced garlic, chopped anchovy fillets, and red pepper flakes to the skillet. Cook, stirring frequently, until the garlic is fragrant and the anchovies have dissolved, about 2 minutes.
Add the canned diced tomatoes to the skillet. Stir to combine and simmer for 8 minutes, allowing the sauce to thicken slightly.
Stir in the halved Kalamata olives and rinsed capers. Cook for an additional 2 minutes to heat through.
Add the cooked spaghetti to the skillet with the sauce. Toss to coat the pasta evenly, adding reserved pasta water a little at a time if the sauce is too thick.
Season with salt and freshly ground black pepper to taste.
Remove from heat and stir in the chopped fresh parsley.
Divide the pasta among plates and serve immediately.