Since Google first made its APIs availabe for any and all developers to use, many quirky new utilities -- based in one way or another on Google -- have surfaced on the web.
One that I've found interesting is Poodle, a tool that spiders any given site and points out "warning" areas that, if improved, could increase the site's ranking with Google. It takes a few minutes to figure out what's going on when Poodle gives results, but eventually you get a feel for it's colour-coded "advice".
Another example of a use of Google technology within a different application is Googlematic, which lets you get Google search results through Instant Messanger programmes, such as AIM.
Some developers have used the Google APIs to create fun sites, such as Googlism. Type your own name in there (or just your surname, if you don't see results) and see what you learn about yourself!
Other spin-off sites/tools are listed on Googuide.