Does Google keep your keyword searches?

Yes! They do. This is taken from Google's Privacy FAQ;

"Like most Web sites, our servers automatically record the page
requests made when users visit our sites. These "server logs" typically include your web request, Internet Protocol address, browser type, browser language, the date and time of your request and one or more cookies that may uniquely identify your browser."

To help keep your searches anonymous and private, the good people at TOR have an easy solution for you. Click here for the instructional video on how to install this software. Keep in mind you should not completely trust TOR, but hey, it gives some peace of mind.

Every search on Google or any other search engine you have ever typed in is recorded by logging your IP address from the search engine you are using, as well as the Internet Service Provider you are using.