During the day, very few places will require that you have a bike light, but at night, most cities and states have some requirements for visibility. You’ll want to check your local bylaws. Certain states require not just a small red rear light on your seat post, but a full light set.
The reality is, if you’re riding a bike in the dark, front and rear lights are critical for your safety. So, even if you can ride legally without them, you shouldn’t.
You should also run your rear light during the day, and possibly even a front light when the weather is poor. A Clemson University study found that cars were much more likely to spot cyclists who were using lights during the day, as well as at night.