Instant messages are to electronic communication what post cards are to snail-mail... Someone who is motivated, and technologically capable could intercept and read your messages, but it's not likely to happen...unless you're involved in nefarious activity, making yourself a legitimate electronic surveillance target.
If you refer to iMessage, only the person you send it to can see it. You can create group messages where more than one can see all the texts. I'm not sure what you refer to as "instant messages".
What he said! ↑↑
Sent from my ancient iPhone 5 (no longer trustworthy)
As stated, only the intended recipient can read the message. Having said that, if that person is careless and leave the phone unlocked and he or she is nowhere near it, then a snoop can gain access to the phone and possibly read the instant message.