Caller ID can be disabled on a call-by-call basis by dialing *67 before the phone number. For example, if you wish to make a private call to 555-555-5555, dial *67 555-555-5555. This service is typically free and can be used by all phone numbers and companies.
Caller ID can also be permanently disabled from a phone line by calling the carrier and requesting a line block. This option is irreversible, so it must be considered carefully. Lines under a permanent line block can show their caller ID on a call-by-call basis by dialing *82 before the actual 10-digit phone number.