It is really more uncomfortable than dangerous to ride in the rain. Just slow down, give yourself a bit more cushion between vehicles, take turns a little easier, use your common sense forgodsake, ride with a little extra courtesy for others, and wear the right stuff—proper rain gear, helmet with face shield, waterproof gloves (rubber kitchen gloves work in a pinch), and waterproof boots (or ones that have been treated with weather proofing goop).
If prepared not scared, pouring rain need not ruin our ride. Challenging the elements fires our instincts, focuses our awareness, and makes us feel more like an animal. Be that beast on a bike and survive these wild streets.