CatLog shows a scrolling (tailed) view of the Android "Logcat" system log, hence
the goofy name. It also allows you to record logs in real time, send logs via
email, and filter using a variety of criteria. It has a widget, can record logs
in the background and has useful colour coding.

It won't work on Android 4.1+ without root access, since apps are not allowed to
access each others' logs.