I came across this while I was browsing something else :

http://www.google.com/intl/xx-hacker/why_use.html
http://www.google.com/intl/xx-hacker/
This one is strange, everything is in "hacker speak", and all the links work and keep that same encoding of the words...

http://www.google.com/3.html
This one is just old. It makes reference to indexing 3 billion pages. Rumor has it they are way passed that number.

http://www.google.com/lucky.html
Reminiscent of the old google, I'm not really sure what this one is.

http://www.google.com/default.reg
http://www.google.com/google_rsearch.reg
These two are just strange because they are registry files for internet explorer settings. I wouldn't expect to see that in the google root directory.

http://www.google.com/ig/currentcomm/current_links_module.html
This one is only interesting because of the reference to the online file backup account...

http://www.google.com/ig/current
there was news a while ago that google are allowing companies to make customized versions of the personalized home page for use by customers and employees
This is nothing more than a hosted home page for the employees/customers of http://www.currentgroup.com/ (an ISP specializing in BoPL)

http://www.google.com/imghp?hl=km&tab=di&ie=UTF-8
This is another interesting encoding of the google page

http://www.google.com/sitemap.xml
Maybe this isn't a big deal, but I was surprised to see this xml sitemap in their root.

http://www.google.com/mozilla/google.xul2
I have never seen this before, so I thought it was strange. Looks like it is for a mobile device or something...

http://www.google.com/ie_rsearch.html
This one looks like what shows up in the IE sidebar at times. Maybe thats what the above one was for too?

http://code.google.com/webstats/2005-12/elements.html
If you like numbers, I just thought this was an interesting break-down of the pages they index and elements of those pages.

http://www.google.com/moms/
http://www.google.com/moms01/
http://www.google.com/googlefriends/may1998.html
http://www.google.com/translate_t
http://www.google.com/googleviewer/loading.html
http://www.google.com/ig/resetprefs.html
http://www.google.com/pda
http://www.google.com/palm
http://www.google.com/pda
http://www.google.com/palm
These don't really do anything, just interesting or strange pages I found.

http://www.google.com/googlegulp/product_line.html
very odd.

here's another cool one:
googlex.jayssite.com
it's just a cool variation of google. it works basically the same

Here, have a search as follows :
http://www.google.com/search?hl=en&q=site%3Awww.google.com&btnG=Google+Search


here