Generally colder is better, so anything recommended to be stored at -20 can also be stored at -80 and may keep for longer. For proteins (antibodies, growth-factors), we always use -80C, but make small aliquots, because they can be degraded by repeated freezing and thawing. Opening the door of your -20 freezer for too long may cause thawing of stored reagents.

It depends on what chemicals you want to store. The best way - to store chemicals in according to manufacturers' recomendations. If you have no possibility to hold reagents in conditions recommended by manufacturer you must to consult them about another acceptable storing conditions. Note that some reagents can be destroyed by change its state of matter and stored in antifreeze which still liquid at -20 but at -80 the transition to the solid state can be occured. In such way some reagents can be destroyed.

Restriction enzymes and other enzymes to work with RNA or DNA come in 50% glycerol that is liquid at -20C but freezes down at -80C. Repeated freezing down usually kills enzyme activity.