Winglets to control wing bending
When I was on a contract at Airbus a few years ago, I went to a lecture on wing design given to the Filton branch of the RAeS.
Winglets, in all their forms, were a significant part of the lecture, and the bit I was previously unaware of, was how they were used to control wing bending and loads on the wing root. A well designed winglet can reduce the bending load on the root, despite generating more lift in the outboard part of the wing. Early Whitcomb winglets may have increased bending loads on the wing to the extent that the weight of the extra structure cancelled out the performance benefits.
As has been noted previously, Airbus are now offering Whitcomb style winglets on the A320, so unless it is just for marketing reasons (customers won't buy the planes without them?), they must now offer greater benefits.
Winglets can also be used to control the torsional loads in a wing; as on, for example, the QinetiQ Zephyr 7 UAV, with its 'Klingon Battlecruiser' wingtip. In this instance the large span (22.5m) and ultra-lightweight structure (50kg AUW) necessitated a tip design which reduced the tendency for the tip to tuck under.