I generally won't leave for a ride if it's raining, but I have been caught in rain many times. Fenders help a lot, particularly if you are just riding on wet roads after a rain. I don't give a huge amount of weight to rain forecasts if the odds are 50% or less. If it's clear in the morning, I will usually bike commute. However, sometimes I will drive when it's clear in the morning if the forecasters are predicting severe thunderstorms and it seems pretty certain. More often than not, the forecasters are wrong, but I don't like riding in thunderstorms.
I drove today partly for that reason, but also because I was just tired. We've been having violent thunderstorms around here lately, and I got caught in one while kayaking over the weekend. I also rode 60 miles on Sunday in high heat and humidity, and just felt like I needed a break this morning.