GIFs are in the middle of cultural comeback. But according to a study conducted by W3Techs, fewer sites are actually using them. JPG is still the most common format by far, and it's holding steady. GIF use is steadily going down, PNG use is steadily going up, and as of today CompuServ's 25-year-old image format has fallen to third place.
This has very little to do with animated GIFs, which is what most people associate with the format; PNG is much more suitable for still images and interface elements (though animated PNGs do exist). According to the study, "while GIF's patent issues [which led to the development of the PNG format] are long resolved, it's the technical superiority that now convinces webmasters to chose PNG over GIF. PNG results in smaller files most of the time, it supports a much wider range of color depths and transparency options. The only feature where GIF still shines is its support for animation."
"For every site that changes from PNG to GIF," it says, "more than 3 sites make the change in the other direction." In September, Rebecca Greenfield at the Atlantic Wire predicated that the internet was approaching "peak GIF." It looks like she was right.
In a comment, Thomas Boutell, one of the creators of the format, does a little victory dance: "When I posted the first draft of PNG (originally called PBF) back in '95, I didn't know for sure that PNG would triumph, but I knew that something would replace GIF. I just didn't realize it would take 18 years. Better late than never!"