Actually, in it's infancy, there were winglets planned. But that was when the 777 was still being considered a stretched 767. Boeing isn't the biggest fans of winglets. At least they used to be. If you look at the 777 wing from a top view, you will notice that the tip is slightly angled outward. Boeing used this technology because in there eyes, winglets weren't necessary. They used winglets on the 744 because extending the wings more was impractical. They latest technology is the "raked wingtip". These are used on the 767-400 and on the coming 777-300ER and 777-200LR.
I'm not a real aeronautical engineer, I just play one on Airliners.net.