Cloudy water from the faucet?

I have regular city water. I have never had a problem in the house I moved into about 6 months ago. All the sudden, last night, we noticed the water from the bathroom faucet was very cloudy and dingy looking. The water in the kitchen appears to be the same way, not quite as noticeable. What should I do? Is the water safe to give to my pets and safe for handwashing and bathing?