I was also following the instructions on http://developer.android.com/training/basics/actionbar/setting-up.html
and even though I did everything in the tutorial, as soon as "extends Action" is changed to "extends ActionBarActivity" all sorts of errors appear in Eclipse, including the "ActionBarActivitycannot be resolved to a type"
None of the above solutions worked for me, but what did work is adding this line to the top:
import android.support.v7.app.ActionBarActivity;