I've previously written about using webcams to monitor your pet when you're away from home. Recently, I've been trying out audio-only monitoring. In some cases, such as if you have a dog that tends to howl when left alone, being able to hear what's happening at home is more than sufficient. Additionally, audio is much less problematic when it comes to positioning and lighting. That is, you can probably hear your dog scratching or whining in the next room, but with a webcam you'd never know that anything was wrong.
One solution is the Evoz Monitor app, for iOS devices. It's particularly handy if you have an old iPhone or an iPad that you leave at home all the time. You install the app on the device that stays home, and on the iPhone you carry, and then you can listen in from wherever you are. (Yes, you have to remember to start the app on the home device, known as the monitor, before you leave.)
Evoz's 2 week free trial is long enough to help you decide if the app is going to work for you. After the trial period, unless you pay for a premium account, you're only allowed 30 minutes worth of monitoring a day, but I've found that limit is approximate, at best. Note that Evoz is designed to monitor human babies, so none of its premium features (such as parenting discussion or crying baby alerts) are useful for pet owners. (My experience confirms that a barking dog does not set off the "your baby is crying" push notification.)
The mic sensitivity (I used an iPad 2 as a monitor) and the sound quality is quite good. You should find it more than sufficient for listening in at home. In fact, if you live in a quiet area, you might want to leave a radio playing at home (if you don't already) just so you can be sure the system is actually working.
I did have problems with the monitor remaining connected and active for long periods of time (several hours), but I wasn't able to narrow the cause of this down to my trial period ending, my iPad locking itself after not being used for a while, or some other random thing. If you start a trial of your own, figuring out the best strategy for leaving the monitoring device turned on should be your first priority. If you find a good solution, please let the rest of us know.