Winglets are a way of increasing wing aspect ratio without actual wing span increases. Typically you get about 70% of the effective aspect ratio increase of the winglet length. As we know from our flight theory, induced drag is inversely dependent on aspect ratio. Therefore you will get a induced drag reduction using winglets.
As induced drag is highest at low speed, clean config, at cruise winglets have less benefit and when you design them you have to balance up the net reduction in induced drag at lower speeds with the increase in skin friction drag which is a function of wetted area and greatest at high speed. So there is no straightforward 'perfect' winglet solution and this is why they all look different (747-400 vs A310) or there are non at all (777)!
Then of course there are all the control issues raised by the other guys...
Hope that helps