Today, favicons appear in many places. These are among the most relevant;
Google displays favicons in both desktop and mobile search results in most parts of the World.
In Chrome and many browsers, it appears on the browser tab when a page from your site is open.
It can appear in bookmarks.
Some services that build an Open Graph excerpt of your page can show your icon.
e.g. Discourse shows the favicon of shared links.
If you drag a shortcut to your desktop, it can appear there as well.
You can do a similar thing to save frequently-used sites on your mobile devices, and it will use the favicon there as well.
