I don't know if they sell these things anymore, but back when I was a wee lad, my dad bought me a RadioShack "300-in-1" kit, where all the pieces had springs on them and you could connect wires between them. It came with a huge manual that showed a bunch (300!) of different circuits.
At the time, I was just fascinated that I could put them together the way I did. Later on though, reverse engineering them really helped to solidify my understanding of how they worked and how the principles could be applied to my own circuits.