Umbrella Today is a site that answers that question for you. It's the brainchild of tech consultant firm thoughtbot. All you have to do is punch in your ZIP code, and you will get a yes or no answer as to whether you'll need to bring that umbrella or not. Of course, you're not always near a computer, so they've turned the site into an iPhone app. The app will not only answer the question, but it will even provide scheduled alerts or push notifications when you need to carry that umbrella.
I love it -- it's simple, practical, and effective. The app is US$1.99, but even if you have an issue with that price, you can set up an email alert on the site for free. Still, a one-time payment of $2 is cheap for never being caught empty-handed in the rain again.