I deal with this issue almost every day here during summer months. A 15-25% chance of rain would be a clear day around here and I would probably ride unless I had other compelling reasons to drive. I usually draw the line at about 50% but the forecasters around here are notoriously inaccurate at predicting rain. I have gotten caught in storms when forecasts called for a 0% chance of rain and more frequently we get no rain on days when forecasts are calling for 60-80% chance of rain.

I disagree with those who are downplaying the risks of riding in thunderstorms. The chances of getting hit by lightning might be slim, but your chances of getting hit by cars are not. Visibility is often very poor during heavy rain and drivers are much more likely to not see you. Add to that the risk from high winds, hail, falling limbs, slippery pavement, etc.

My most useful iPhone app is called MyRadar and simply shows radar views of storms. I consult this app frequently, particularly during the afternoons when my ride home is nearing. I often will delay my commute to allow time for a storm to pass and sometimes catch a ride home with coworkers. The worst situations are severe thunderstorms that "train" over the area and can produce rain, flash floods and lightning that last for hours. This happens often enough around here that I am very cautious about riding when radar shows approaching storms.