Not all glues are created equal; a glue designed for plastic may not be the best choice for cardboard. Glues that adhere well to cardboard are generally the same glues designed for paper or wood, since all three materials are porous. As with paper, too much glue may make some types of cardboard soggy, so apply thin layers of glue to cardboard for best results.
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Cardboard Gluing Basics
Cardboard -- from thin cardboard similar to cardstock on up to thick corrugated sheets -- requires an adhesive designed for porous materials. The best type of glue for cardboard is a PVA or polyvinyl acetate glue, such as school glue or wood glue. For thin, small pieces of cardboard, glue sticks designed for scrapbooking may suffice. Wood glue provides such a strong bond that it is used even for cardboard boat-building contests. To glue one piece of cardboard to another, apply a stream of glue over one piece of cardboard, then brush it into a thin layer with a foam brush or even your finger. Press the second piece of cardboard onto the first. Weigh the glued area down with a heavy weight such as a book for several hours.