I believe favicons today are even more popular than in the past.
Part of the issue I believe you are running into is how favicons are displayed. It isn't that they are less popular, but the location or how they are displayed may have changed.
Here is the rundown on where they are displayed.
Address Bar: Firefox v1 - 12, IE 7+, Opera v7 - 12 and Safari
Address bar drop down list: Firefox
Links bar: Firefox, Chrome, IE 5+, Opera 7+
Bookmarks: Firefox, Chrome, IE 7+, Opera 7+, Safari
Tabs: Firefox, Chrome, IE 7+, Opera 7+
Drag to Desktop: Firefox, Chrome, IE 5+, Opera 7+
(List from Wikipedia)
You also have to consider that favicons are now playing a larger role because of mobile devices. When someone bookmarks or pins a site to their screen it will use the favicon. I find that having favicons set for mobile are great because it shows a logo or icon vs seeing the page crammed into a small icon on the screen.
Bottom line: Favicons are not going anywhere and I highly recommend programming them for both desktops and mobile devices.