I believe they can only connect your searches if you are logged in while searching. Otherwise, of course they can collect data on anonymous searches but not ones that would be specific to you.
I hope I'm wrong.
I hope I'm wrong.
So assuming you use google more than once every 6 months they can keep a running log of your searches, and as soon as you log in to any google service with that cookie they will associate it with your account (I'm guessing).
If you clear your cookies reguarly or use incogneto it's not an issue.