When you plug your iPhone into a Mac to charge it, you'll get a message telling you that the iPhone is paired to another Mac if this is not the Mac to which you sync your iPhone and it won't let you continue. If you want to charge your iPhone and you want to avoid this situation, you have two ways around the problem.

First, if the Mac in question is a laptop, if the lid is shut you can plug in your iPhone to charge it and you won't get any trouble.

Second, set a passcode for your iPhone in the settings screen. If you do this, when you plug your iPhone in you'll be asked for passcode and it'll tell you that you can't connect until the passcode is entered. If you just dismiss this dialog, you won't be able to connect to your iPhone, but you will be able to charge it.