Rain has never hurt a runner (although lightning can), but what you wear and how you take care of yourself after a run does make a difference.

• If the temperature is under 45 degrees Fahrenheit or so, wear a Gore-Tex or similar type of jacket on rainy days. Gore-Tex doesn't allow rain to penetrate the jacket and get through to your skin, but it also can get hot, so check the temperature before heading out on warmer rainy days.
• If the weather is hot and rainy, wear as few clothes as possible so that you aren't lugging heavy, wet clothes throughout your run.
• Wear a baseball cap to keep your head dry for as long as possible.
• Whether you're soaked to the skin or just a little damp when you get back from your run, change into dry clothes immediately, before you stretch. If you're still cold, take a warm shower as soon as you're done stretching.
• If you see lightning before you start running, put off your run until later in the day or run inside on a treadmill. If you see lightning while on your run, seek shelter immediately. Stay away from trees, too, which may be hit by lightning.

Keep in mind that wooden bridges and other surfaces may be quite slick after a rainstorm -- almost like a patch of ice.