I occasionally carry two rods to fish a stream, one for streamers and nymphs and one for dries, although normally i carry the rod i think i need most and just suck it up and use it if my guess is wrong. I generally accept the notion that the more stuff i carry with me the greater the likelihood i will lose or break something.
But here is a little bit differing twist on carrying multi rods. i fish on lakes a lot, maybe half of my fishing, and most of it from a boat. Much of the fishing i like to do on western lakes is driven by calibaetis hatches and spinner falls which are notorious for their short schedules. They often start at maybe 10 or later and sometimes last as little as 30 mins to an hour. So when i have all the lights on i take multiple rods rigged for various aspects of the hatch, nymphs, emergers, duns, spinners, and often more than one rigged with a dry and dropper so when i break off or tangle, i can put the rod away and get out another and keep fishing. You cannot carry this too far or you will look like a bass pro fisherman with a whole boat full of rods. But a couple extras does help. i also carry some pre-rigged setups of dry and dropper to replace a tangle or breakoff; i wrap those little rigs around a foam pad kept in a plastic box i bought somewhere, brand name not remembered.
