I hope this thread is useful to some. If the information in here grows to become substantial, perhaps the mods can make it into a sticky. Of course, I'll leave this up to them... People, please feel free to correct and add to this, this first version is just a very rough draft.
It is rather overwhelming keeping track of all of the different virtualization and emulation products out there, the platforms they run on, the differences between para and full/native virtualization, or simply what options (paid and free) are available to accomplish a given task. I've said something in one of these threads a while ago about Xen that I now know to be false, so hopefully we can use this thread to collectively educate and enlighten. It can be difficult to keep everything straight!
Here is a little something I put together, feel free to expand upon it. As a preface, I have included information about products that run under Linux and Windows as well, as many of us are still on PowerPC hardware, but have access to some old PC hardware we can use...
Firstly, if you want to run an OS or application unavailable for your processor family, you will need an emulator. For running an OS or applications on the same processor, you will want virtualization software. Apple's Boot Camp is neither - it is simply a set of drivers for booting a Mac in Windows. This guide is not about Boot Camp.
The most common OS X based virtualization products are Parallels and VMWare, but there is also the open source VirtualBox and QEmu (I believe Virtualbox is based on QEmu). The differences between each come down to the bells and whistles and features offered. I have not used VirtualBox.
Under Windows and Linux, you can download the 30 day trial of VMWare Workstation, and continue to use the disk images you created under Workstation in the free VMWare Player for as long as you like. If you have an old PC, this is a great way to run different operating systems and applications. VMWare is easy to install and setup in Ubuntu, and likely Windows.
Other virtualization products include Microsoft's Virtual PC, and QEmu with the kqemu kernel module under Linux.
Para vs. full/native virtualization
If you have an Intel processor with the VT chip (I believe all Intel Macs do), you can run a virtualized environment that offers full/native virtualization. This means that the "host" OS does not require modifications in order to run the virtualization software. This means that software like VMWare should run just fine on this hardware under any OS, but some OSes may not work with various virtualized environments on hardware without the VT chip (if you have an AMD processor, the equilvilent there is called "Pacifica"). There is a good Wikipedia article
compared the different virtual machines which you should look at, but the bottom line is that if you do not have VT or Pacifica, you should be after para-virtualization solutions (which are actually a little faster than full/native virtualized solutions).
For the Mac, the most common emulator was Virtual PC. Virtual PC was bought out by Microsoft and is now sold as a virtualization product for Windows. This product was eliminated on the Mac, so you might fare better looking into Bochs or Qemu. The performance hit is so great in doing this though, that your efforts would likely be best spent looking into virtualization instead.
Server focused virtualization software
Xen and VMWare Server are both solid products focusing within this space. Virtualization is becoming increasingly popular among server admins, since virtualized environments are extremely easy to deploy, secure, recover from disaster, and can help consolidate servers on a set of servers attached to external storage options (e.g. RAID, SAN, etc.). Many hosting providers are offering virtualized servers rather than full dedicated servers, as this can be cost effective approach.
VMWare Fusion offers some experimental DirectX hardware acceleration, which would be useful for 3D software and game playing. I don't know much about any of this at this point though since I haven't tested this. There is a video of some games in action running under VMWare Fusion on YouTube. Apparently this support is also present in VMWare Server and VMWare Workstation, I believe.
Running individual applications
If you wish to run an individual Windows application, you may not need to install a full OS in a virtual machine to do this. Many applications run in Wine, and a commercial preconfigured solution called Crossover Office will run many applications right out-of-the-box. If you are on a budget, it might be worth researching running your application under Wine before splurging for Crossover Office, as Crossover Office is literally just Wine with set configurations for running supported applications. There are many guides available for running apps under Wine.
I haven't played around much with Wine under OS X on an Intel Mac (running on a PPC Mac requires Darwine, which incorporates Qemu for doing processor translation - last I checked, Darwine was non-functional), but I have played with Wine under FreeBSD (which shares many of the same underpinnings as OS X). I was able to get some things to run, but many other things wouldn't.
Wine is really more of a Linux solution, last I checked. However, it will allow many applications and games to run quite well. If you need some sort of guarantee, consult the database at WineHQ, or investigate whether your app is supported by Crossover Office.
Because of the lack of hardware acceleration, using a virtual machine is not a great solution for gaming right now. However, products such as Wine, Cedega, and the Transgaming subscription service will allow you to run many Windows games under Linux. There is an OS X port of Cedega in the works, I don't know exactly where it is at.