I could not get the new web apps preview to work properly on my 12.04 system, so I decided to remove it using the following code:
sudo apt-get install ppa-purge sudo ppa-purge ppa:webapps/preview sudo apt-get remove gnome-control-center-signon signond signon-keyring-extension signon-plugin-oauth2 signon-ui libunity-webapps-chromium unity-chromium-extension unity-lens-gdocs unity-lens-photo unity-scope-flickr xul-ext-webaccounts xul-ext-unity xul-ext-websites-integration
However, this does not remove already created web apps, which are still accessible via the Unity Dash. In my case the Google Reader and Reddit web apps are still available in the Dash.
Any help completely removing these web apps would be greatly appreciated.