Well they are so vital the 757/767/777 don't even have them.
From reading various articles and books about aircraft design, it appears the use of winglets, depends on the engineers. The wing can be designed with the same efficiency without the use of winglets as a different wing has with them. The 777 uses a raked wingtip to give the same effect. For older designs, it may be easier to attach winglets (real ones, not the tiny A320 type) like the new ones showing up on 737s. On new aircraft, it could go either way. Apparently adding winglets can be like adding several more feet to each wing, which reduces drag and increase lift.
Are they essential? It doesn't look like it.
I'm not an airline pilot, or an aeronautical engineer. Just someone who was very interested in this topic before.