OpenBSD is an outstanding OS, well-documented, simple, consistent and tightly integrated, with good defaults (no need to adjust much on a default installation before having a working system for everyday use). While I partially agree with Nia, one has to give credit where credit is due, and OpenBSD, throughout all its history as a R&D UNIX with a focus on code correctness, cryptography and security, deserves praise for the many good ideas they came up with (OpenSSH, PF, CARP, W^X....).
OpenBSD has invested a lot of energy in desktop support and tends to just work (often including graphics -with the exception of nvidia-, ACPI, touchpads). The OS comes with a really nice set of native software allowing one to easily deploy simple and secure servers. It actively supports several CPU architectures (less than NetBSD), and some happen to be very well maintained, especially SPARC64, with a nice deamon to manage LDOMs, and macPPC.
Generally speaking, OpenBSD is regarded as an optimal choice for small to medium size appliances directly facing the internet and is particularly suited for firewalls, routers, DNS, DHCP, VPN/Tor, Web, mail servers.
On the other hand, their attitude and philosophy (their pride) make them always want to advertise each and every feature or component of their OS, as well as any commit merged into mainstream adding even the most negligible feature. Just have a look at their official innovations page. There's a undoubtedly lot of remarkable efforts mentioned there, but also a lot of entries which do not appear as much 'important' . NetBSD or Linux could host similar 'innovations' pages (and the list would be long); the question is, however, what purpose would such an effort serve?
NetBSD devs maintain a patched monolithic X version in base (as well as a modular one inside the pkgsrc tree), and yet they didn't renamed it with a flashy nick seemingly coming from a Infocom fiction^
Instead OpenBSD devs imported and patched Xorg (for a rootless default setup, to enhance privilege separation), then imported and patched XDM by removing XDMCP, and decided to name the former hack Xenocara and the latter Xenodm. Hope you've never come across a OpenBSD fanatic, not seldom clearly clueless about the OS design and internals (naturally, and fortunately, most of the fanboyism has nothing to do with developers; it largely comes from young KISS UNIX zealots migrating from Linux), bragging about the many features of Xenocara, 'a stripped down Xorg fork with many indispensable security improvements, devoid of all the cluttered nonsense, because X is flawed and broken...., blah, blah'.
I'm probably speaking too much and need to be quicker now. What I wanted to stress is that much of that incredible popularity you seem to refer to is at least in part built upon a series of fandom-driven half truths and misconceptions, as well as a very good amount of official advertising campaigns, fueling the hype.
OpenBSD overall feels like a big boring monolithic piece of software. Default installation and default settings are strongly recommended and devs tend not to like exotic configurations. All of their software appears built with the same philosophy in mind. Software should be installed via binary packages, no much left to say. At time feels like a OS built by developers for themselves, kindly shared for others to use (but if you dare ask a question, it's mostly RTFM). They're not interested in your feedback, if you want something to change you'd better come on the mailing lists with a PR ready to be reviewed, at least.
Whatever is left orphaned without somebody eager to take up full-time maintainership, is quickly deprecated and it doesn't take much for it to be removed. Linux compat and bluetooth met such a fate. OpenBSD has no multilib, so no wine and their hypervisor (vmm) is still very limited both in its capabilities (IIRC each VM cannot use more than a core at a time) and in supported clients. The only FS available is FFSv1/2, which provides no journaling (though it has soft updates), no snapshots and no TRIM support.
NIH is also one of their problems. One thing I miss on OpenBSD is tmpfs (no, mfs is not a valid replacementt). Julio Merino created NetBSD's tmpfs long ago, and their implementation was quickly imported in FreeBSD. tmpfs was later ported to OpenBSD too, but left unmaintained after a while and eventually removed.
To sum up, not much to discover, not much space left to hack around, not many cool and obscure features to explore. That's the main reason which I don't like OpenBSD for (performance aside, since the difference in my experience is not so significant on desktop and can be overcome, unless you run a high-end workstation and have some heavy workload to undergo or performance requirements to meet).
In this regard NetBSD is quite the opposite, pure freedom. Among Linuces, I love Slackware because it shares with it this same approach: "here's your fresh UNIX framework, do what the hell you want with it".
And then there's pkgsrc. I would have never discovered NetBSD hadn't it been for pkgsrc; it represents for me alone a good reason to stay already. There are many things I find brilliant and extremely useful about that packaging system, but I really need to go now, so perhaps we can discuss it another time.
^ I remember, from the good times when I was still following BSDtalk, that Matthieu Herrb stated he had discovered that word while looking into Latin names of fish species; he liked it and decided to borrow it. Truthfully speaking, as one who studied ancient Greek, I can tell that name is of Greek derivation for sure and means something like 'foreign face'.