It feels like every website today wants to send you notifications, regardless of how big or small they are. Visit a page in Chrome, for instance and you'll often see a dialog in the top-left asking you to allow notifications. If you're sick of seeing these, it is possible to rid yourself of them forever... or selectively, depending on your mood.
Woe is the Chrome user who has an overflowing Bookmark Bar — or worse, that single folder they use to store anything interesting they see online.
If you don't want to receive notifications ever, then the solution is simple.
Crack open the Settings page, scroll to the bottom and click "Advanced". Then under "Privacy and security", click "Content Settings..", which will expand into a screen like the one below.
Select "Notifications" and when the new screen opens, just hit the "Ask before sending (recommended)" option, which will change to say "Blocked". Once this is done, you'll never again be prompted by websites for notification permissions, nor will you see notifications for sites you may have previously allowed.
This page also lets you control notifications for individual sites. You may notice quite a few are there already — these are sites that you have blocked or allowed in the past.
Now, if there are some sites you do want notifications for, say Slack or Trello, you can block and unblock sites piecemeal. The easiest way to do this is to visit the site in question and click the "Secure" text / encircled "i" to the left of the URL (see below).
Hit "Site settings", which will the show a page of options for that particular domain. Change the "Notifications" setting to either "Ask", "Allow" or "Block", depending on your preference.
Finally, if you want to make sure you never receive notifications from Chrome on your desktop — also known as "native" notifications — you can kill them via
chrome://flags. Browse to the flags page and look up "Enable native notifications". Change it from "Default" to "Disabled".