Contrary to popular belief, there is no right to privacy against your employer enshrined in the Constitution. Generally, you must rely on state laws to guarantee your privacy. Typically, what is protected from a search by your employer depends upon what they are searching for. If it is something that is owned by your employer, then they may search it. If it is owned by you, then you have greater protections against a search.
For example, your employer may search your desk, office, locker or any other storage area owned by the employer. This also includes your work computer and any files stored on it, even if you store personal pictures or files. Your employer may search your email, assuming it is a company email, and all emails that you send from that address. And again, this includes any personal emails you may send or receive. This also includes all other forms of electronic communication such as phone calls and texts from company phones. Sometimes states have mutual consent laws that require an employer notify you if your call is being recorded.
Contrary to a search of your desk by an employer, there are protections in place against more invasive searches such as polygraphs and drug tests. Generally, your employer may not subject you to pre-emptive polygraphs. A polygraph is a machine that can tell if you are lying. There are some exceptions if you work in security or pharmaceutical industries. Furthermore, your employer may subject you to a drug test. You are free to refuse to submit to the test, but an employer is also free to refuse to hire you.
It is also important to keep in mind that the rules governing your relationship with your employer will typically be included in an employee handbook. If you work for a large corporation or company, your employer will usually have uniform rules dictating when and how they may search you. If you believe that you were subject to an illegal search by your employer, then you might want to consult with an employment attorney. Typically, you must submit to reasonable searches by your employer, but that does not mean you must agree to every search.