New or prospective hams should know that there is no expectation of privacy in amateur radio. Anything that you communicate legally can be received by other people.
Ham radio involves transmitting intelligence (voice, Morse code, text data, pictures) to be received and understood somewhere else. By its nature when you transmit a RF signal it goes out into the world (maybe beyond) where anybody with the proper equipment can receive it.
If you are transmitting on a repeater or other well-used frequency someone else is likely to copy you. However, the chances of someone monitoring a random frequency and mode is rather slim. People scanning repeaters or tuning around the HF bands may listen but if what they hear isn’t interesting they may move on. So the likelihood of your QSO being listened to depends on frequency, mode, and content. Basically, others can listen but this doesn’t necessarily mean that they are doing so.
Hams cannot legally encrypt or disguise their messages for privacy as this violates rules against secretive transmissions.
The two reasonable exceptions are when sending control commands to orbiting amateur satellite repeaters and when operating a hobby model such as a RC airplane.
Digital (RTTY, PSK, JT, FT, Olivia and the like) and video (ATV, SSTV) signals cannot be interpreted by ear so there is some privacy from the general public listening in. But anyone with the right equipment can decode these and follow along. While these modes are technically encoded, they are not secretive because they are commonly used.
You also cannot secure privacy via anonymity. Stations at both ends of a message must legally identify themselves
Of course, if someone really wants to be secretive and violate US amateur radio Part 97 rules by encrypting their transmissions or not identifying, that is a possibility. We hope that all hams choose to play it straight and follow the rules, in which case anything that you say over the air can be picked up.
Our best advice is to not worry about privacy. Don’t say anything over the air that you don’t want others to hear. If you must do so, use a different means of communication.