Seeking QGIS equivalent of ArcGIS Erase tool?

Is there a QGIS equivalent of the Erase tool in ArcGIS Desktop?

The Erase tool:

Creates a feature class by overlaying the Input Features with the polygons of the Erase Features. Only those portions of the input features falling outside the erase features outside boundaries are copied to the output feature class.

Answer

Yes there is.

It's called Difference, and you can access it by doing Vector > Geoprocessing Tools > Difference.