AegisLab Antivirus Free scans the apps on your Android device and warns you of any problems.
The program offers three scan types: installed apps, full system (apps and your SD card), or "custom" (a particular folder on your SD card). Scans can be scheduled, too. However you launch them, the final report will warn you of "suspicious apps", as well as any with ads (you're recommended to run them "only when necessary").
Tap any of these "problem" apps and you can uninstall it directly from Antivirus Free. Or, if you're entirely sure it's safe, you can exclude it from future scans.
Once you've run your initial scan, AegisLab Antivirus Free then checks new apps as they're installed, notifying you of its results.
If you like the core technology, AegisLab Antivirus Premium ($7.99 a year) extends it with anti-theft, antiphishing, contact backup, remote GPS Location to find a missing device, and more.
Should you trust them? We've not tested the app enough to say for sure, but in February 2014 VirusTotal announced it's adding AegisLab as a file scanning engine, so the company clearly has some very capable technology.