Text messages (also known as SMS, short message service) and email are both safe, but have limitations to their security and privacy. If confidentiality is critical for your communication, it is best to encrypt your email or use the secure email form on a Web site when available.
Text messages and voice are encrypted while in the air. Mobile operator managed wireless networks are secure and maintained by IT professionals, and the carriers put very strict controls in place to prevent individuals from misusing network technology. It is extremely unlikely an individual text message would be read, and it would take high level system administrator access to do it. Since U.S. law requires that all telecommunications carriers and equipment providers enable government law enforcement agencies to conduct lawful surveillance when needed, however, the capability clearly exists.
As to email, again it is possible that a system administrator at the company hosting your email could potentially read your mail. In addition, email moves through the Internet on servers controlled by thousands of government, education and private sector organizations. It is possible, though unlikely, that a system administrator somewhere in that path could capture and read email. It would be difficult and random, as individual emails move across the Internet in different paths.
If you want to be very careful, you should encrypt your email, especially if the content is highly confidential. This is particularly true in a corporate environment for sensitive subjects like earnings forecasts, layoffs and raises. Encryption is a way to scramble the data with a mathematical process, called an algorithm, and a digital key that you control. Only people that have your key can read your encrypted email. To know more about encryption, see How can I protect the files on my PC?
If you are sending highly confidential email to someone like your bank, a credit card company or the IRS for example, a very safe practice is to use their online email form rather than your normal email account. This is far more secure than using regular email, because your message is encrypted between your PC and their server as it travels through the Internet. Be sure to look for https:// in the browser address bar. The S is for secure. For more information see, How does Internet security work?
If you ever receive a mobile text message asking you to click on a link and enter in your account information, delete it immediately. It is a phishing scam. In addition, never communicate sensitive personal information like your social security number or credit card information over SMS.