Linux
Linux distros (different versions kind of like Home Basic vs. Ultimate for Vista, each has their strengths and weaknesses) all use the same building block called a kernel. A kernel drives the computer, and in Linux's case, is easily changeable by the user. The top three environments are GNOME, XFCE, and KDE. Kind of like if Vista could change between an OS X look, Vista look and Win 95 look without major reconfiguration. Linux doesn't get the support that Windows or Mac get from hardware, some manufacturers don't want to support Linux at all, but Linux users are some of the most resourceful people, so most everything works. Example distros include ubuntu(user friendly) , gentoo(confusing, but oh so fast), KNOPPIX(live cd/rescue cd), Fedora (more professional ubuntu), Slackware(been around for a long time), Puppy/Damn Small Linux(works on old computers with limited resources), iPodLinux(its linux on your iPod), PCLinuxOS(user friendly), Kubuntu/Xubuntu(KDE/XFCE instead of GNOME on an ubuntu base), Debian(ubuntu and Knoppix are based off of this)
BSD
FreeBSD, OpenBSD and PC-BSD are similar to Linux distros and use some of the same software, but are closer to Linux's kernel's inspiration than Linux itself. They are compatible with just about any Linux program, and can run just about anywhere.
Unix
Commercial professionally done OS's that run on large servers. Also Linux can be called *nix and Un*x, because the Linux movers and shakers don't want to get paid money just so it can be called a Unix OS.
Windows
Its the most common and most infuriating OS on the market. Avoid at all costs.
Classic Mac
Built by Apple, abandoned after OS X decided to use the BSD kernel instead of building a new version of Mac 9.
OS X
Based off of the same thing as the BSD and Linux OS's OS X is a new step for Apple Computers. All of their releases are named after members of the feline family. THe most current one is 10.5 Leopard. Hard (though not impossible) to run on anything but an official Apple computer.
My current favorites are: XP MCE, yeah its windows, but if you keep it simple it will let you watch movies with non'Linux compatible hardware; ubuntu 7.04 This is my primary OS currently and works very well on my laptop, round April I expect this to change to 8.04; Knoppix, it comes in handy when I have to go rescue Windows from itself; and finally, iPodLinux just for ridiculousness's sake