Where can I download the Google Road network as shapefile?

No, Google's road data is proprietary and is not distributed in a GIS capable format. This is because Google spends a lot of money keeping their GIS accurate and current, and distributing it for free would allow Google's competitors (e.g. Microsoft, MapQuest, Apple, ESRI) to download it. This would forfeit Google's competitive advantage in the web mapping world.

OpenStreetMap does offer downloads of their entire road dataset. The "Downloading data" Wiki page has some more information. The data download page is here. If you only need data for a single region or country, I recommend using the prepackaged downloads from geofabrik.de.

Options

Buy a commercial product- TeleAtlas or Navteq (Google now use TeleAtlas - originally it was a mix of both)

Google do provide Downloadable data but only for MapMaker Countries

https://services.google.com/fb/forms/mapmakerdatadownload/

shapefile or KML format:

(Mapperz did a blog about this in April 2009 http://mapperz.blogspot.ca/2009/04/google-maps-map-maker-vector-data.html)

Or use OpenStreetMap [Recommended]

http://wiki.openstreetmap.org/wiki/Planet.osm (for commercial use allowed)

I would not recommend doing copy of those data. It is not FREE. The license did not allow you to use it outside of google maps.

You could try extract some data using the google maps webservices but this would be allowed only for use with your client map.

You can buy street information from some companies or use free available data published.