Only if you logged in to google and perform those activities. For me, I can only see this history of youtubes viewed if I had signed in on those days, or else it would not associate those history to my login.
Granted, it's going to store all those activities regardless of one is signed in or not, just that they're visible to you.
I'm against Google to know everything I do, but my point being Google is not the only company on earth to do something like this. Apple is another one, and so do Microsoft, Yahoo, etc. If you have connected GPS that provides real time traffic, weather, etc, those companies also log requests you submitted, and they also store your location, speed, etc without you pushing any buttons or interactions with your device, so they use it to provide and calculate traffic and routes. What's more, they store it at such a detailed level that you haven't thought about. When you shop at Amazon, it saves all your search whether with your account, or as cookies if you did not sign in. Just a couple more examples.
Google is an easy target just because it's in the business to collect data. For those that are not, you think they don't track and log your information? Think again.
I'm not a sucker nor cool-aid drinker, just stay alert and learn ways to disable these "features" wherever and whenever possible. One can't be ignorant and whine about what companies are doing behind the scene and hope these things will go away - they simply won't, and they will get worse, whether it's Google, Facebook, Tweeter, Groupon, Apple, you name it!
For those so sensitive about it, don't use internet and don't use smartphones. Heck, even activities on dumb-phones are tracked nowadays, and you do know wireless carriers store all your call history regardless of what kind of phone you use, right?
Or else, try live the live like Osama bin Laden... stay in the house all day long and only keep in touch with the rest of the world via the good old messengers.
After all is said and done, do you still feel like having fun with Siri?