Telephone companies provide users with "call blocking service", which can be activated permanently or temporarily by entering code (such as *67) before dialling the desired number. This will not give away your phone number to the person you have called, instead the person would get a "Withheld"/"Private Caller" notification on his telephone set's Caller ID. If somebody has been calling you from a "Private"/"Withheld" number, you can trace the number through a variety of ways.
Contact your local telephone carrier to get the code that redials the last number that called your phone. In North America it is usually *69. Try dialling this number, and if someone picks up the phone, explain how you got a call and inquire about the name of the person who might have called you. You can also get names from the recording machines that might be operating on the number you dialled, if an operator doesn't answer.
Make a search for the person by entering his name in a search field of a search engine, such as Google, or a people search database such as Pipl, if you retrieved a name through the recording.
Make a reverse number search if you retrieved a phone number through the recording. A free way to do that is by entering the number in the format "333-444-5555" into the Google search field, and writing down the details, such as the caller's name and address.
Contact your telephone company to get an anonymous call blocking service. People calling from blocked number will not be put through your telephone until they unblock their number. This won't block the "Masked Caller IDs" from calling cards, and pay phones.
If you receive a threatening phone call from a private/anonymous number, contact your phone service provider. The company will then take action according to its policies regarding the matter. They might trace the caller or ask you to file an official complaint with the local law enforcement.