DOS: the one I grew up on. It's a no-frills attached, text only operating system. It was good for what it needed to do at the time: execute programs, manage the file system, etc.
Windows: I'm sure you've worked with this one. The operating system for the computer idiot and the hated bane of the computer nerd. Unreliable, major security issues, decent networking capability, intrusive, rude, and just a monster IMO. About the only redeeming feature is that it's the only OS that can play almost every computer game on the market.
Windows NT, 2000, XP: slightly better incarnations of Windows. More secure, more reliable, and very good networking capabilities.
Mac OS: Windows for Mac machines only really really good.
Linux/Unix: There are at least two dozen different builds of these, most available free of charge. These are insanely reliable, incredibly stable, massively good OSs. If you're runing a webserver or network server there simply is no other alternative than a *nix OS. I've only had a few months exposure to one of these OSs (Sun Microsystem's Solaris) but I loved every minute of it. It was so damn fast, and never crashed once. The networking was unbelievable and the system never got b****y like windows does. There are other people on this forum with far more experience with linux/unix who I'm sure can be a little more informative on this subject.
BeOS: The mysterious OS. I've heard of it, I've seen TV ads for it, yet I've never seen it (or even a screenshot of it). I have no idea what it can do.