The short answer is: it depends.
Given the multitude of jurisdictions around the world, it's really difficult to give a comprehensive answer. For now, I'll just focus on the U.S.
The main law covering commercial email is the CAN-SPAM Act. The Federal Trade Commission provides an easy-to-understand compliance guide you can consult. To steer clear of illegal behavior, they advise the following:
- Don’t use false or misleading header information.
- Don’t use deceptive subject lines.
- Identify the message as an ad.
- Tell recipients where you’re located.
- Tell recipients how to opt out of receiving future email from you.
- Honor opt-out requests promptly.
- Monitor what others are doing on your behalf.
You should read the full guide before you start sending your email campaigns.
For recipients in other countries, you should make sure you understand the local laws in order to make sure you comply.