What is the exothermic reaction of superglue with cardboard?
I believe this is due to the fact that cyanoacrylates polymerize by anionic (or sufficiently strong neutral nucleophile) addition. In particular, they react with hydroxyl ($\ce{-OH}$) groups; paper, being primarily cellulose, is abundant in hydroxyls. The bond formation involved in the polymerization reaction is inherently exothermic (generating a $\ce{C-O}$ bond on initiation and many subsequent $\ce{C-C}$ bonds as the polymerization proceeds), and with a large surface area and many reactive groups, I could certainly imagine the reaction being surprisingly violent. The Wikipedia page on cyanoacrylates notes its reactivity with cotton fibers (again, being chiefly composed of cellulose), and the MSDSs for various similar compounds warn of exothermic reaction with paper and similar materials (q.v., 1, 2, 3).