Two of the exhibitions I've enjoyed most recently are the Formula 1 technology display at the Science Museum and The Childrens War display at the Imperial War Museum. These were engaging in different ways;
The F1 exhibit showed how the technology has flowed down into mainstream engineering like carbon fibre tables and electronic tyre pressure sensors. It was laid out in such a way as you could see the product alongside the F1 technology that influenced it. Images and text described things in greater deatail. As their 'crowd puller' the museum had displayed a McLaren F1 car hanging upside down from the entrances ceiling which looked amazing.
The Childrens War exhibit aimed to tell the story of the hardships of the war through the eyes of children. It was seperated into areas corresponding to each childs personal story and engaged the visitor by displaying their toys, clothing, photo's and personal voice recordings of their heartfelt and touching stories.