Google's decision to allow nearly every site to send notifications to users regardless of their preferred platform can be unendingly bothersome since users tend to see notification requests every time they load up a page. There is a way to turn all of those off completely though and it's actually very easy to accomplish.
The problem arises because a tap on the page itself instead of on the 'Block' or 'Allow' button -- accidental or otherwise --will hide that request away, ensuring that users will see the request again next time they visit that site. Like so many things Google does, site notifications themselves can be exceptionally useful but with tradeoffs. For more rambunctious sites, usefulness goes out of the window relatively quickly.
The only obvious way to stop notifications is to either allow site notifications or turn them off when a request appears. That can be easier said than done but also isn't the only way to turn them off. Users can choose to completely block them off altogether before notification requests even begin to appear.
Turning notifications off ...all of them
Turning site notifications off across all of Chrome or Chrome OS is not difficult, requiring just a few quick steps. For users on desktop or mobile versions of the browser, the first step is to click or tap Chrome's three-dot menu at the top-right-hand side of the UI and then to select "Settings." Chrome OS users can also choose to open the Settings application instead and the UI will be nearly universal across each variant.
Mobile users can skip this next step since the "Advanced" options are extended by default. For desktop and Chromebook users, scrolling to the bottom of the resulting interface and clicking or tapping "Advanced" will reveal further options and the setting to be sought is under the "Privacy and security" subheading. More directly, it's found via a tap on the box labeled "Content settings."
From there, users on either the Chrome smartphone app or on other platforms need to tap or click on the "Notifications" option to unveil the appropriate UI. The resulting page shows off which websites notifications are blocked and allowed for individually but a toggle at the top of the page -- labeled "Ask before sending (recommended)" -- is the key to turning off or on all notifications by default.
Switching the toggle over changes the label to "Blocked" and effectively kills all notifications across the board. However, it doesn't appear as though a change in either mobile or Chrome for desktop instantiates the change across an entire account. So users will need to follow the steps to accomplish that on other platforms that they use.
Leaving notifications on for your favorite sites is easy
While turning off notification requests can and will save a lot of users a lot of time and not-insignificant headaches, there are always going to be a few sites that users will undoubtedly want to continue seeing notifications from. After following the steps to turn all of the notifications off, reactivate them for individual sites is straightforward.
To accomplish that, users simply need to navigate to their favorite website and look for the lock-shaped favicon in the Omnibox next to the site's URL address. A click or tap on that icon will bring up site-specific settings options. On mobile devices, a further click on the 'site settings' option is required to get to the appropriate option but desktop and Chrome OS users only need to look for new "Notifications" option with a drop-down menu at the top of the resulting settings card.
The setting will default to "Block" but clicking on that and then selecting "Allow" will turn notifications on from that individual site.