Heat oil in Dutch oven. Add onion, green pepper and garlic; cook over medium-low heat until vegetables are tender, 8 minutes. If too dry, add water, 1/4 cup at a time.
Add beef, chili powder, cinnamon and allspice; cook, stirring, until meat is no longer pink, 10 minutes. Add tomatoes, chilies, vinegar, salt and sugar; cover and simmer 1 hour.
Cook spaghetti according to package directions. Drain.
To serve, arrange hot spaghetti on large platter. Spoon chili over spaghetti. Top with cheese and green onion. Serve with crackers.