Yes, you can have a site show a Pagerank and not be in Google’s index.
Here is an example of a site showing PR3 in the Google Toolbar:

This same site is not in the Google Index:

Google has recently released an updated version of Google Toolbar for Internet Explorer (IE), now at version 6 Beta. The main features of this new toolbar is it’s Quick Search Box (QSB). Quick Search Box brings Google strength on search and navigation to not only web pages, but whole computer and Internet, as QSB provides [...]

Google Product Search which has been formerly known as Froogle added a brand new option to restrict the results to sellers that offer free shipping. So that means when a shopper enters his location, the service can automatically calculate the tax and shipping charges for any particular product.

Google Base blog recently wrote that sellers can [...]

A new news aggregation service called Addictomatic has been released. You can enter any topic in addictomatic such as “google” or “comic book” or everything else and it shows you a customizable instant news overview of those topics from a lot of different sources. The news bits are shown as little widget boxes and pulled [...]

Google Street View has been recently enabled for France. There used to be different panorama photos from the Tour de France route, but now there are regular pictures, from Paris, Lyon, Toulouse, Marseille, Nice and Lille. Now it provided you with four zoom levels, and as usual for recent Street View imagery, Google tries to [...]

When you are trying to embed a YouTube video, you can add a “start” pointer to define the number of seconds at which the video should start, as SEM blog explains. Here’s a sample code:
<object width=”425″ height=”344″><param name=”movie” value=”http://www.youtube.com/v/11Fl9ZVJ7B8&hl=en&fs=1&start=15″></par am><param name=”allowFullScreen” value=”true”></param><embed src=”http://www.youtube.com/v/11Fl9ZVJ7B8&hl=en&fs=1&start=15″ type=”application/x-shockwave-flash” allowfullscreen=”true” width=”425″ height=”344″></embed></object>
This parameter will only work if you are trying [...]

The Google toolbar already has a built in feature that lets you make Gmail as your default email client. But if you don’t have the google toolbar installed this is how you can do it in the latest version of Firefox.
associate “mailto” links in web pages with Gmail, so that when you click on [...]

It seems like Google has recently removed the dictionary link in search results for at least a portion of users, or perhaps all users, In past, when you searched for a word in the dictionary – for instance “house” – there would be a link leading to a definition in the top blue bar. [...]

If you have installed Google Chrome and want the latest releases of Google’s browser Chrome quicker than the usual official Beta updates, you can now download a special program called “channel switcher” executable from Google. Simply Run it on your Windows machine and you’ll see a dialog where you can check the Dev option and [...]

Google Presentations has recently undergone a complete redesign, making it look more like recent versions of the Google Docs text editor.
If you’re new to Google Docs, watch this video to learn more about creating and collaborating on documents: