I use all sorts of two fly combinations. On the Bighorn, I generally use a scud/sow bug point fly with a midge or mayfly nymph dropper. During the summer, it seems like hopper/dropper. With the dropper being some sort of beadhead nymph pattern. Sometimes I'll use a attractor dry behind the hopper, if I know the fish are keyed to the surface.

About the only time I use a single fly is when I'm streamer fishing.