I do have a rain bike because my "good" bike is a Litespeed with all-Campy components. It does get caught in the rain occasionally but I don't want to make a habit of it. Also, there is no room for fenders or a rack of any kind.
My rain/snow/beater is a Surly Cross Check with fenders, a rack, 700-32 treaded tires and built up with a combination of parts box leftovers and "Anything On This Table...." closeout specials. I did treat the frame and fork internals very thoroughly with Frame Saver when I first got it so there is no problem with internal rust.
It's heavy as an anvil but worry free. I hose it down after a particularly dirty ride as long as it's not so cold the water will freeze on my driveway. I do take care to wipe off and relube the chain after each wet ride but that's the only routine care it gets.