Current caselaw allows employers unrestricted access to their employees' e-mails on devices owned or provided by the employer. The rationale is that employees have no "reasonable expectation of privacy" in e-mails because they are generally stored on the employer's computers (or third-party servers paid for by the employer) and can be easily accessed by the employer.
On June 18th, in Quon v. Arch Wireless, the Ninth Circuit Federal Court of Appeals issued a ruling distinguishing text messages from e-mails and limiting an employer's right to access such text messages even if the service is paid for by the employer or the messages are on devices owned or provided by the employer.
The underpinning of the ruling is that unlike e-mails, text messages are generally intended to be instant communications that are not typically thought to be stored. Therefore, the participants in a text message conversation maintain a reasonable expectation of privacy in the content of that communication (however, there is still no expectation of privacy in the headings of a text message, only the content). A text message conversation is akin to an old-fashioned voice call over a telephone line, in which the participants maintain a reasonable expectation of privacy because they do not contemplate that a record of the conversation is being kept.
If your employer wants to look through your e-mails, text messages or any other communication, or they already have, be sure to consult an attorney to insure your privacy rights have not been violated.