Combine bread cubes, garlic, green pepper, water, and salt in container of an electric blender; process until smooth. Remove cover; continue to process, adding oil in a thin steady stream. Add tomatoes and vinegar; process until smooth. Cover and chill thoroughly.
Pour Gazpacho into chilled individual serving bowls; place 1 ice cube in each serving. Serve with several of the following condiments: (about 1/2 cup each) chopped cucumber, chopped tomato, chopped green pepper, chopped green onion, chopped hard-cooked egg, and croutons.