An app equivalent of logcat from the terminal. You can filter by importance in the settings: see only errors or view general debugging info. The result can then be filtered by keyword so if an app has problems you can send just the relevant logs to the developer. But watch out, the filter remains in place unless you remove it!
This application is fork of aLogcat and it works only on devices running Android 4.1+. If you have root access full system logs are shown, otherwise only this applications logs are shown.