Collaboration Site (no Publishing features activated)
You'll most likely have to edit the master page of the site with SharePoint Designer 2010 and set the "Visible" attribute of the control containing the "All Site Content" link to "False."  Alternatively, you might look at using the Content Editor Web Part with the appropriate styles embedded in it.  However, you'd then have to add this web part to every page that exposes the "All Site Content" link.  Certainly, this is not ideal.  Either way, it's much easier to hide when Publishing features are turned on, which is discussed in the next section.

Publishing Site

1. Create a new CSS file and add the following style to it.

   .s4-specialNavLinkList
   {
     display:none;
   }

2. Save this CSS file to your SharePoint site's "Site Assets" library.  If you don't have one, save it somewhere else in the site that makes sense.

3. Navigate to the home page of your SharePoint site.

4. From the Site Actions menu, select Site Settings.

5. Under the "Look and Feel" section, click "Master page.”

6. Scroll all the way down to the bottom of this page.

7. In the "Alternate CSS URL" section, select the radio button labeled "Specify a CSS file to be used by this publishing site and all sites that inherit from it."

8. Click the "Browse" button to browse to and select your CSS file.

9. Click "OK."

10. Navigate back to the home page of your site and you should now see that the "All Site Content" link is no longer visible.