As an AI language model, I do not have access to real-time data and cannot provide recommendations or rankings. However, some of the major airlines that are known for offering convenient and efficient connections for multi-city or round-the-world travel itineraries include Emirates, Qatar Airways, Etihad Airways, Singapore Airlines, Cathay Pacific, Japan Airlines, ANA (All Nippon Airways), Turkish Airlines, Air New Zealand, and Qantas. These airlines have comprehensive networks, advanced booking engines, and seamless transfer processes for connecting flights, making them popular choices for travelers who need to hop between multiple destinations or book complex itineraries.