Ampere is a free app built for Android devices running Android 4.0.3 and up. WonderHowTo first brought the app to my attention last month, but I've just now been able to test it. The goal is to help you troubleshoot suspect wall-warts and USB cables.
After installing the free app, launch it and wait until you get a reading containing the milliamps your device is using. Keep this number handy, as you'll need it in a minute. Next, plug your phone or tablet in to charge. Wait until you have a new reading, and write down the number. Now, look on the AC adapter itself for its output reading.
Each AC adapter has a set output. For example the unit I tested will push out 500 milliamps. I know his because it's listed in fine print on the AC adapter itself.
When I connect my Nexus 6 to it, I get a reading of between 200 and 240mA. When I take that number and combine it with the average amount of milliamps being used when the device is unplugged (around 300mA) I can surmise the charger is working properly.
Should the number not match up, either the USB cable or the AC adapter is likely faulty. I could swap out either part of the equation, and measure again until I've figured out where the issue lies.
The Play Store listing includes devices the app isn't compatible with, as well as general guidance of the app not being capable of providing precision accuracy. In other words, don't throw away your multimeter.