It's still not very popular due to it's size in bytes comparing to all other formats. At the moment the APNG format is supported by most major browsers now. There is also APNG (or animated PNG) format which appeared because of the GIF limitations, but was denied by a number of comminities in the beginning. The animation objects are usually used in GIF format which is very popular due to it's history, but the loading images in SVG and CSS format are getting more and more poplular because of infinite size scalability - they can have any dimensions and relatively smaller size in bytes.
Being an critically important part of web-site and application design and usability, mostly the animations are used to show that something is loading on the background (e.g. Loading GIF or, so called loader gif is an animation that indicates a loading process on a web-site or an application.