How can I automatically clear logcat output before each run in Android Studio?

This can be customized for each existing run configuration you have defined. Instructions for enabling this feature are given below:

Android Studio 1.4 and later

Check the checkbox located at:

Run -> Edit configurations… -> Miscellaneous tab -> “Clear log before launch”

Android Studio 1.3 and earlier

Check the checkbox located at:

Run -> Edit configurations… -> Logcat tab -> “Clear Log before launch”