If you use a transparent echoing proxy this can show you all http traffic Charles and fiddler are two good example, I recommend Charles.
Looking at new work traffic when I type "app" into chrome I see the following request
http://clients1.google.co.uk/complete/search?client=chrome&output=chrome&hl=en-US&q=app
GET /complete/search?client=chrome&output=chrome&hl=en-US&q=app HTTP/1.1
User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US) AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.53 Safari/525.19
Accept-Encoding: gzip,deflate,bzip2,sdch
Cookie: SID=DQAAAIYAAAATI2S8dKFp5KGjAbyGxNaA4R4qbW24KzjW3jHTJOqIewCl64OqpBjnj7ReJ1aoFBA_rJ5h32jTrwD_xFTEgVfSqqXMfh_1e8bIcvLgz8qSRnXxWNUepTD90fXeHh0KfKtI9EkdkjgOPT2a9_1DJBlyzpOItI7o-fD5zQ6fjA9YdlC4TeCZqlsjbD6O8nXR5mg; PREF=ID=427f2a6420c4c235:U=19879741710226bb:TM=1224000168:LM=1240414461:S=kGvdcM6wirgoK_L7; NID=21=QOXGkbW3w-orrYC5IFOpPW9jEwdTz4oNJ6Pem0lcyFlvzxZHQgyYsf63kR2g4Pq62H0xWR8l7mF03GLgIJoPAZPIlMFG-ghig5ManOtWA7f3bqqq1eNtWSYyZYo4Ja5z
Accept-Language: en-US,en
Accept-Charset: ISO-8859-1,*,utf-8
Host: clients1.google.co.uk
With the response
HTTP/1.1 200 OK
Content-Type: text/javascript; charset=utf-8
Date: Fri, 24 Apr 2009 08:06:54 GMT
Expires: Fri, 24 Apr 2009 09:06:54 GMT
Cache-Control: public, max-age=3600
Content-Encoding: gzip
Server: Auto-Completion Server
Content-Length: 175
["app",["http://www.apple.com/uk/","apple","apple store","apple trailers"],["Apple (United Kingdom)","437,000,000 results","37,700,000 results","995,000 results"],[],{"google:suggesttype":["NAVIGATION","QUERY","QUERY","QUERY"]}]
Charles knows about JSON so translates this into a pretty format
Screen Shot Of Charles http://img2.imageshack.us/img2/2926/suggestionsforapp.png
See full size
As you can see (easiest the full size image) this google service returned 4 results, one of type NAVIGATION(http://www.apple.com/uk/) and 3 of type QUERY(apple, apple store, apple trailers). It also contains more information for each a description for the NAVIGATION result(Apple(United Kingdom)) and the number of results for each of the QUERY suggestions(437,000,000 37,700,00 995,000).