Cook beef, onion, and green bell pepper in a large nonstick skillet over medium-high heat until browned; stir to crumble. Stir in diced tomatoes and next 9 ingredients. Bring to a boil; cover, reduce heat, and simmer 30 minutes, stirring occasionally.
Divide cooked spaghetti among serving bowls. Spoon chili over pasta; top each with 1 tablespoon each of cheese and onion and 1/4 cup crackers.