We use to say that there are around ten billion curl installations. It makes a good line to say but in reality we, of course, do not have any numbers that exact. We just estimate and guess based on observations and trends. It also depends on exactly what we consider "an installation". Let's elaborate.
The project being Open Source and liberally licensed means that just about anyone can redistribute curl in source format or built into binary form.
The curl command-line tool and the libcurl library are available for download for most operating systems via the curl web site, they are provided via third party installers to a bunch and they come installed by default with even more operating systems. This makes counting downloads from the curl web site completely inappropriate as a means of measurement.
So, we cannot count downloads and anyone may redistribute it and nobody is forced to tell us they use curl. How can we figure out the numbers? How can we figure out the users? The answer is that we really cannot with any decent level of accuracy.
Instead we rely on witness reports, circumstantial evidence, on findings on the Internet, the occasional "about box" or license agreement mentioning curl or that authors ask for help and tell us about their use.
The curl license says users need to repeat it somewhere, like in the documentation, but that's not easy for us to find in many cases and it's also not easy for us to do anything about should they decide not to follow the small license requirement.
The command-line tool curl is widely used by programmers around the world in shell and batch scripts, to debug servers and to test out things. There's no doubt it is used by millions every day.
libcurl is what makes our project reach the really large volume of users. The ability to quickly and easily get client side file transfer abilities into your application is desirable for a lot of users, and then libcurl's great portability also helps: you can write more or less the same application on a wide variety of platforms and you can still keep using libcurl for transfers.
libcurl being written in C with no or just a few required dependencies also help to get it used in embedded systems.
libcurl is popularly used in smartphone operating systems, in car infotainment setups, in television sets, in set-top boxes, in audio and video equipment such as Blu-Ray players and higher-end receivers. It is often used in home routers and printers.
A fair number of best-selling games are also using libcurl, on Windows and game consoles.
The libcurl binding for PHP was one of, if not the, first bindings for libcurl to really catch on and get used widely. It quickly got adopted as a default way for PHP users to transfer data and as it has now been in that position for over a decade and PHP has turned out to be a fairly popular technology on the Internet (recent numbers indicated that something like a quarter of all sites on the Internet uses PHP).
A few really high-demand sites are using PHP and are using libcurl in the backend. Facebook and Yahoo are two such sites.
Nothing forces users to tell us they use curl or libcurl in their services or in the products. We usually only find out they do by accident, by reading about dialogues, documentation and license agreements. Of course some companies also just flat out tell us.
We used to collect names of companies and products on our web site of users that use the project's products "in commercial environments". We did this mostly just to show-off to other big brands that if these other guys can build products that depend on us, maybe you can, too?
The list of companies contains hundreds of names, but extracting some of the larger or more well-known brands, here's a pretty good list that, of course, is only a small selection:
Adobe, Altera, AOL, Apple, AT&T, BBC, Blackberry, BMW, Bosch, Broadcom, Chevrolet, Cisco, Comcast, Facebook, Google, Hitachi, Honeywell, HP, Huawei, HTC, IBM, Intel, LG, Mazda, Mercedes-Benz, Microsoft, Motorola, NASA, Netflix, Nintendo, Oracle, Panasonic, Philips, Pioneer, RBS, Samsung, SanDisk, SAP, SAS Institute, SEB, Sharp, Siemens, Sony, Spotify, Sun, Swisscom, Tomtom, Toshiba, VMware, Xilinx, Yahoo, Yamaha
The Google Youtube app, the Google Photos app, Spotify, Instagram, Skype (on Android), bundled with iOS, Grand Theft Auto V, Fortnite.