It depends on the kind of riding you want to do. If it's a short commute on a roadster you take an umbrella, and a mud flap on the front fender will help for the puddles. For really heavy rain you can take a poncho that goes over the handlebars.

If you want to go fast and sweaty on a road cycle, it's probably important to stay warm when you get wet, and a little fender for the spray the rear wheel aims precisely at your crack will make it more comfortable. I don't have much experience with that kind of cycling, but in general look on what kind of surace your going, white lines are slippery but also regular tarmac corners with a negative cant can be dangerous in the wet. Some pavements are much more slippery than others, usually if it looks a bit like a mirror it grips like mirror, but find out from the safe side. As long as you keep the bike about vertical and the wheels don't lock there's no problem, so brake on the straight and corner slowly. Go easy on the front brake, if the front wheel locks up on a slippery surface, you're probably going down, a rear wheel lock up can be corrected.