Your ever have something you were talking about getting and then it pops into an add even before you started doing any searching? I've had it happen twice that I can remember. Its freaky
One thing to be aware of is that even if you don't actually search for something, but you type it into the search form, (or any form) they can track and store that ... even if you never click search. If you move your mouse over something, that can be tracked as well, even if you don't actually click on it.
Think about this scenario, which probably most of us have done. You're on an e-commerce site and you decide to order something. You add it to the cart and then go to the checkout form. You type in your name, address, credit card number, etc, but decide not to order it. Maybe you hit the "Cancel" button, or type in a new URL in the browser, or close the browser ... whatever ... All the information you just typed in, could still have been captured and saved by the site, even though you didn't submit the order!
There's software called "Full Story", and probably others, that a website can use that tracks absolutely everything you do on the website. Every mouse movement, every keystroke, etc. I'm not 100% sure of what the privacy laws are in this area, but if you go deep into the disclosures and privacy notices on most websites, they tell you that your activity on the website can or may be monitored.