That's still a thing, it's just the design of widgets from app to app is disparate, usually visually clashing if multiple widgets are used. Not as clean and uniform as Windows Phone tiles.

There is an Android launcher (launcher 10, i think) that offers tiles, and some of them even live tiles. It's okay, not quite the same slick experience though.

They haven't been removed per se, but fewer apps tend to have them. Most Google apps have high quality widgets.

Widgets are alive and kicking.