As of May 2015, there is no special glue that works on all types of plastic. Nonetheless, there are two types of adhesive used to bond most plastics, including reactive adhesives and non-reactive adhesives.
Reactive adhesive contains a base resin and a catalyst that reacts when mixed together. Epoxy comes in two separate tubes and does not harden until combined. This chemical reaction separates it from non-reactive adhesive, which hardens with no reaction. Non-reactive adhesives include hot adhesive, which hardens as the heat departs the bonding agent. There are many tools available for purchase to make applying adhesives easier including adhesive kits, brushes and patch kits.