This topic come up all of the time. To answer your question, yes, they work, but...
They are definitely not the latest aeronautical fashion accessory that every well dressed aircraft must have. They are not appropriate or worthwhile for all wing designs. Marcel Dassault, the famous French aircraft designer, said that properly designed wings don't need winglets. It seems to me that few, if any, new aircraft with "clean sheet" wing designs, such as the Boeing 777, incorporate them, while airframe manufacturers will incorporate them on "old technology" designs (i.e. B747-400, B737, etc.) that they're trying to improve aerodynamically. Winglets are much cheaper to incorporate on older airfoil designs because they have minimal redesign and recertification costs.
I'm not an aeronautical engineer by any means, but I've flown thousands of hours in turbojet aircraft that were essencially identical except some had winglets and some didn't. My personal observation is that whatever small performance gains they provide often is usurped by the handling penalties they impose. Additionally, from what I've heard and read, their design is still somewhat of a "black art" and claims for increased efficiencies can often be tenuous at best.
Just for grins, I went to the Aviation Partners Boeing website, (They're the folks that do the winglets for the Boeing 737.) they list as one of the benefits of winglets:
"MODERN DRAMATIC APPEARANCE...Blended Winglets bring a modern look and feel to aircraft, and improve customers' perceptions of the reliability and modernity of the airline.
One of the problems associated with winglets is that they happen to be the current aeronautical fad much like "T-Tails" were 25 or 30 years ago. Remember, that was when you saw T-Tails introduced on several single-engine Pipers, the Beech King Air F90 and several other designs where the advantages of a T-Tail were (are) extremely hard to see. Unfortunately, IMHO, winglets fall into the same category.
Do winglets have their place? Of course, but they need to be thought of as "Aerodynamic Band-Aides".