Earlier quoted context omitted.
First, I'd rather Google not have it. I consider Google having it to be a breach of my privacy. But besides that, any time someone clicks an ad, Google gives information about that person to the advertiser.
You can absolutely tell google not to store your information. When you buy a shoe with your credit card at a store you are giving your personal information, isn't clicking on an ad similar?
...except for all the times when Google did collect and store your information despite you telling it not to (look online for location tracking on Android).