OpenBSD is one of three *BSDs. It was forked from NetBSD in 1995 by TheoDeRaadt, one of the core NetBSD developers, when he and the rest of the team had a falling out. You can read the rather bitter saga, described from Theo's side.
The OpenBSD project permanently hand audit all their code. Everyone, and the Unix world in particular, owe them a lot for spending lots of time actively looking for bugs and security issues and removing them, as well as promoting use of secure alternatives to common protocols, even writing their own implementations where necessary. An example is OpenSSH, written to get rid of Telnet in favour of SSH.
For whatever reason, OpenBSD has the annoying default of using csh(1) as the shell. csh(1) doesn't support tab-completion or history (you can't even push up to go back to the last command!). It is advised to use the ksh(1)? shell that is also installed.
The primary source of revenue for the OpenBSD project is the sale of official ISO CDROM images. If you want a free version, you either have to go looking for a non-official image, or make your own. Though you can generally find images about on the various mirrors, these usually lag behind the current release by a few version numbers. You can install an one of these old versions then do an upgrade, but this can be difficult to get right. You could also make your own image. The simplest way to install OpenBSD for free is to download a boot floppy image from the official site, and let the new system retreive the rest of the tarballs via ftp during its install process- this assumes you have a system that can boot from a floppy and has high-speed network access.
If you are upgrading from OpenBSD 3.3 to a newer version, beware that the binary format has changed and there isn't compatibility turned on by default. Read the upgrading docs carefully so you don't hoze your system.