Many plants produce natural adhesive, just for example the sap of the Artocarpus altilis, which was used as a waterproof glue in ocean faring canoes in Polynesia, and the exterior of the fruit of Pisonia brunoniana that was collected and used for trapping birds by sticking their feet to branches. There are scores of other examples.
I am currently working on bio based adhesives for cellulose insulation. Currently guar gum, modified starch, and casein are good candidates. Here is an article on the subject: www.fpl.fs.fed.us/documnts/pdf2010/fpl_2010_frihart007.pdf