When I try to export an Android app as an APK, eclipse suddenly crashes without any clear error message. I experienced this issue with Android ADT plug-in in Eclipse sometime back and found the solution that time. Today, with a new version of the Android ADT plug-in, I faced the same issue and took a long time to find the solution by googling. It was my mistake that I didn't write down the solution in the first time. Today, I'm doing it. The solution was so simple. We have to disable automatic building functionality of Eclipse before we export the APK.
From the menu bar in Eclipse, goto Project->Build Automatically and remove the tick. Now we can proceed to export the APK without any issue. After exporting, I can put the tick again.