Since the invasion of the Amazon Echo, collectively as a society we've been weary of Alexa stealing our information and sending it out to the masses. While that, and an automated Alexa uprising, hasn't happened yet, Amazon has slipped up and accidentally shared some personal info with people it shouldn't have.
A man in Germany requested his personal data from Amazon and received the data of someone who was not him. This slip up was a result of human error, but previous leaks of information have been the result of Alexa misunderstanding something as a command.
If you're trying your best not to send a recording of a very out of context conversation to the wrong person, there is a way for you to change some of Alexa's settings.
One of the biggest steps you can take is denying Alexa access to your contacts when setting up your device. If you have already set up your Echo and given the device access, you have to call Amazon customer service at 877-375-9365 to have them remove it. I know...no one wants to pick up the phone, but its either have a quick conversation to get things fixed or deal with your personal info possibly being shared with others.
It's also recommend that you change your "wake word," so that Alexa starts listening to a word other than her name. Amazon gives you other pre-set wake words like computer, amazon, or echo.
If you really want to protect yourself, you can manually turn off your Echo's microphone by pressing the mic button on the top of the device. If you're using Alexa often, keep the volume up high too, so if you end up recording a nasty message you can catch it before it gets sent to anyone.