Prepare spaghetti according to package directions. Reserve 1/4 cup of the spaghetti cooking liquid. Drain spaghetti and return to pot; keep warm.
Meanwhile, in a 12-inch skillet cook garlic in hot oil over medium heat for 1 minute. Add tomatoes. Cook, uncovered, for 2 minutes. Add peaches. Cook 4 to 5 minutes more or until peaches are just soft, stirring occasionally. Stir in olives, basil, salt, and peppers; heat through.
Add peach mixture to cooked spaghetti along with reserved spaghetti cooking liquid. Toss to combine. Season to taste with additional salt and pepper. Serve warm or at room temperature. Sprinkle with almonds just before serving.