For the whole bike, it's possible to get a bike cover. I use one when it rains at work when commuting, but it's too heavy and bulky to tour with, plus I'm not sure where to stash 40 square feet of wet bike cover.
I have in the past carried a cheap, plastic tarp with gromets. Maybe 5x7 or so. Comes in handy when there is no dry ground to sit on. You can also string it between trees to create a dry place to cook. I have also used it to cover the bike. It won't completely cover the thing, but if you use bungees I can get most/all of the important parts of my 60 cm bike covered. It folds down small enough to fit under your my tent, which goes on my rear rack parallel to the bike.