Linux

The Linux OS is so good it's amazing it is free. There are several distributions that provide nicely packaged software that works well together. My personal favourite distribution is Fedora, but Ubuntu also looks good. I have used several others including Debian and Slackware. Unless you know what you are doing stick with either Fedora or Ubuntu, both are excellent.

BSD

There are several different BSDs: OpenBSD, FreeBSD

Solaris

Sun recently released Solaris 10 as a freely available Operating system.

Items marked with (nyt) indicate I have not yet tested it. I've heard
it's good (so it has made it on the list) but have not yet tested it
myself.