[disposablename]

IE10/11 let you pin any website to the taskbar with its own icon, complete with notification overlays: https://msdn.microsoft.com/en-us/library/gg491738(v=vs.85).a...

[lerpa]

Same for Chrome: http://www.geekpen.com/wp-content/uploads/2016/12/Chrome-Mor...

Probably Firefox also has this.

[SlySherZ]

I can confirm for Firefox. Right click the tab -> Pin Tab. It shows up as a symbol only (hides the title) leftmost tab and never goes away.

Here's more info, with images of how it looks like: https://support.mozilla.org/t5/Learn-the-Basics-get-started/...