All modern web application stacks run as well on Linux as they would on OS X, if not better, so there is no advantage to running OS X and lots of downsides.
You need to run OS X on Apple hardware, and they haven't made a blade server for several years, so you'd be stuck with either the mini or the Mac Pro, either of which is going to be expensive for the computing resources you get. You also can't fit them neatly into an enclosure.
Also, if you ever wanted to move your infrastructure to the cloud you'd need to move to Linux anyway.
I can think of no valid reason to use OS X server to host any kind of web app.
Not true, there are several Mac based hosting companies, offering a mix of physical and virtual servers.
Running it on non-Apple hardware is legally questionable at best (the EULA forbids it, if this part of the EULA is applicable in your country is a question for a lawyer), Apple doesn't do server hardware anymore, it costs money and you don't get support or special software from Apple for server-usage for it, and since nearly nobody runs it as a server OS it probably isn't very high on the priority list to support that usage for other software vendors or open-source project.
A lot of things probably will work well since they are made to run for developer usage, but if you do not absolutely need integration with something apple-specific or just want to reuse an old mac lying around for a hobby project it doesn't give you anything over other OSes as a normal web server.
Many of Apple's own web sites run Apple hardware for outward facing, large scale serving (I used to work there).
At the end of the day, Unix is Unix.
I run nginx on OS X on a number of Mac Minis without issue and long uptimes.
Does that mean Mac Mini? Or Custom Hardware like Xserve.
http://photos.imgix.com/racking-mac-pros
And not directly what you asked, but a thread that comes to mind is this one, where an unnamed company (presumably Mathworks) built a rack of Macbook Pros for testing purposes.
An entire colocation facility that runs Mac minis. It looks fun.
I can confirm this (I work at MacStadium). We've got 1. a large number of CI SaaS companies that run their OS X/iOS builds on our hardware and 2. at least several hundred companies that run their own custom build tools or Jenkins on individual or clusters of Mac minis, Xserves, and Mac Pros in our data centers.
We have no interest in scaling on OSX and plan to port to linux. It's an interim type of thing.
We've since abandoned this practice as there is no Apple hardware suitable for it. We still run some Mac mini servers for things that do not run on any other OS, but definitely not web sites/apps.
I definitely don't have millions of users, but there are hosting companies that do mac only. You can ask them if they have large clients.
(My needs are a node.js based site on virtualmacosx.
I had written something locally on Mac, and it depended on things that OSX did different than Linux, and decided I didn't have the time or inclination to fix it, so went with VMOSX.)
We've got customers of all sizes. It started out with just individual developers and small teams using our solutions so they didn't have to spend capital and IT resources on their own Mac hardware. Many are still here with Mac minis rented or colocated.
Now though, we've got fortune 500 customers, many enterprise tech companies, and a growing number of unicorns joining the service since they can't do internally what we can do at scale in data centers with the Mac Pro. A lot of these customers are using us to test iOS apps with large clusters of dedicated Mac Pros connected to SAN.
[0]: We mostly serve customers that need Mac hardware for app development and CI/CD. We also have HP bladeservers, though, as a few companies have moved their entire infrastructure to our data centers or have migrated from Mac hardware to generic Linux systems and don't want to leave due to certain features we can offer.
I really like OS X, I've been using it on my personal and work computers for 9 years. But for server sit is Linux all the way.