I suspect it depends on the specie of fish targetted, weight of backing, and how often backing gets in the water.
For inshore species, I'd make a small loop on the fly line by simply folding it back on itself, lashing with some 6/0 thread, adding a drop of crazy glue, and finishing with a short length of shrink tubing.
On the backing, I'd make an 8" loop with either a treble surgeon's knot, spider hitch, or bimini twist. Then, you can change out fly lines very easily.
For offshore species, best to visit the search engines or offshore forums, like Dan Blanton's for ideas. Like the moderator indicated above, folks will have 'pet' styles of connections, regardless of specie or location.