I found it exhilirating to keep flying in one direction, more or less, until I eventually got back where I'd started. Plus, it was a great opportunity to combine trips to places that wouldn't ordinarily make for a single trip. For me, the contrasting harmonies of Paris and Hong Kong, Dublin and Bali made for an especially satisfying set of places to visit.
Plus, the mileage opportunities can be immense, and the planning (which can be as much or more fun than actually going) can be a full-time job.
Finally, it's a lower-cost way to fly in premium cabins. A Boston-London round-trip in 1st class would cost me over $12,000(!); conversely, I can fly 1st class around-the-world with an amazing itinerary for a bit over $7,000 -- that's flying RTW 1st-class for 60% the price of a BOS-LHR trip!