====Update 2023====
Google favicons are back. Yuck!
Use this selector in Adblocker Plus to hide favicons from Google. (follow the guide below but switch out with the selector below)
google.com##.H9lube
=================
Annoying little Google! I just noticed when using Google to search it shows all these annoying and mostly ugly favicons next to the url in the search. After doing some Googling apparently there is no way to really turn this off.
It’s suppose to be experimental. But it’s so freaking ugly Google! Stop experimenting on me already!

Free easy way to fix this. Adlbocker Plus. If you aren’t using this already you get so many benefits. Notably no Google ads in your search. And one that I can not live with, no youtube ads! Ive been using an ad blocker for so long that my whole youtube experience has been ad free! Since they didn’t really have ads before I started using it. Once you have it installed you can actually create custom rules. The easiest is to just click the extension icon and click block element. Then hover the element you want to block.

Now this won’t let you pick the favicon directly, but if you just select the title part.

Then just replace the text with google.com##.xA33Gc

Done! No more favicons. By the way you can use this on many other sites as well. A cool way to get rid of elements on the page you don’t like. Ive done it with sites that try and block content. If it’s just CSS and HTML that is blocking it, you can use adblocker filters to remove the element completely from the site and it’s permanent. (or until you turn off that custom filter in the settings)