In the building of a strip boat, people usually freak out when I tell them that the glue they use to bond the strips together doesn't need to be waterproof. There is a good reason for this. The strips are covered with fiberglass and epoxy which is effectively both the structure and waterproof coating for the canoe. Elmers, Titebond and others make good carpenter's glue (Sometimes called "yellow glue") It works just great and the bond is stronger than the wood around it.
There are places where epoxy, polyurethane, resourcinol or other adhesives would work better - usually, I'm talking about the stems, decks, and trim - places that might or might not get a good coat of epoxy.
Still, for the most part, plain old wood glue works great and cleans up nicely!