Elysian Shadows

So I have noticed over the last few years I've gotten really strange advertisements whenever I go anywhere on the internet.

I bought myself a Turtle Beach headset last year, and I did not plug it into my computer or afaik search it up online. Somehow I saw the first Turtle Beach headset ad in my life on a webpage. I went and searched computer hardware last week, now I see tons of hardware which is similar in value/function to what I was looking at. I even typed in something on a document on my computer and saw a recommended youtube video with that word in it! The word is very specific and it was used multiple times in the document. There are so many "coincidences" everywhere I go its alarming.
These ads appear to know things about me and my computer it can't know, at least not legally.

Can a virus do something like this? Why would it do that? I know the major search advertising is Google. They're ads are pretty much ubiquitous throughout the internet. But how can it know I just plugged in a Turtle Beach headset? How can it know about what I'm writing on my own private computer? Am I just being paranoid? Can someone explain to me what's going on, if these are really just coincidences, googe just making ads, or something more sinister?

Well, I registered my google account on my cell phone. Some time later, I was browsing google play, logged into my account, and there was a bar on the left which said: "This app will work on your..." and then it listed my cell phone brand, model and my telephone company. That was scary...

As far as things you typed outside of your browser, sounds like coincidence. Even if there were a keylogger on your computer, there is no way Google served ads would have access to the logged information (they are a large corporation whose actions are watched closely for privacy breaches).

However, Google does serve personalized ads by default. If you are using Chrome, signed into Gmail, or searching on Google, Youtube, or any other service hosted by Google they will use that information to customize your ad experience.

For more information on Google's privacy policy and a detailed overview of what information they are using and how to opt out of certain services please visit the following URL:
http://www.google.com/policies/privacy/tools/

This is linked from the page above, but of particular interest is your Dashboard:
https://www.google.com/dashboard/?hl=en

I would check your browser plugins and remove any you aren't sure of and do a malware scan/removal. Just to be on the safe side. Even if it is just coincidence these things don't hurt to do.