Back in March 2015, I asked friends for a forecast on how much HTTP traffic that will be HTTP/2 by the end of the year and we arrived at about 10% as a group. Are we getting there? Remember that RFC 7540 was published on May 15th, so it is still less than 4 months old!
The HTTP/2 implementations page now lists almost 40 reasonably up-to-date implementations.
Since then, all browsers used by the vast majority of people have stated that they have or will have HTTP/2 support soon (Firefox, Chrome, Edge, Safari and Opera - including Firefox and Chrome on Android and Safari on iPhone). Even OS support is coming: on iOS 9 the support is coming as we speak and the windows HTTP library is getting HTTP/2 support. The adoption rate so far is not limited by the clients.
Unfortunately, the WGet summer of code project to add HTTP/2 support failed.
(I have high hopes for getting a HTTP/2 enabled curl into Debian soon as they've just packaged a new enough nghttp2 library. If things go well, this leads the way for other distros too.)
Server-side we see Apache's mod_h2 module ship in a public release soon (possibly in a httpd version 2.4 series release), nginx has this alpha patch I've already mentioned and Apache Traffic Server (ATS) has already shipped h2 support for a while and my friends tell me that 6.0 has fixed numerous of their initial bugs. IIS 10 for Windows 10 was released on July 29th 2015 and supports HTTP/2. H2O and nghttp2 have shipped HTTP/2 for a long time by now. I would say that the infrastructure offering is starting to look really good! Around the end of the year it'll look even better than today.
Of course we're still seeing HTTP/2 only deployed over HTTPS so HTTP/2 cannot currently get more popular than HTTPS is but there's also no real reason for a site using HTTPS today to not provide HTTP/2 within the near future. I think there's a real possibility that we go above 10% use already in 2015 and at least for browser traffic to HTTPS sites we should be able to that almost every single HTTPS site will go HTTP/2 during 2016.
The delayed start of letsencrypt has also delayed more and easier HTTPS adoption.
Still catching up
I'm waiting to see the intermediaries really catch up. Varnish, Squid and HAProxy I believe all are planning to support it to at least some extent, but I've not yet seen them release a version with HTTP/2 enabled.
I hear there's still not a good HTTP/2 story on Android and its stock HTTP library, although you can in fact run libcurl HTTP/2 enabled even there, and I believe there are other stand-alone libs for Android that support HTTP/2 too, like OkHttp for example.
The latest stable Firefox release right now is version 40. It counts 13% HTTP/2 responses among all HTTP responses. Counted as a share of the transactions going over HTTPS, the share is roughly 27%! (Since Firefox 40 counts 47% of the transactions as HTTPS.)
This is certainly showing a share of the high volume sites of course, but there are also several very high volume sites that have not yet gone HTTP/2, like Facebook, Yahoo, Amazon, Wikipedia and more...