This is a job for ... Wikipedia!
Now that the obvious stuff is out of the way...
Linux runs fine as a guest on every VM host I've used, so I'm going to assume that you're referring to Linux as the host operating system. I'm also going to assume x86 or amd64 hardware.
Platform virtualization breaks down into two major forms: Desktop virtualization and Server virtualization. Both types will allow you to load and run multiple OS instances as guests that virtualize their I/O through the host OS. Desktop virtualization concentrates on providing a highly interactive console experience for each of the guest VMs, while Server virtualization concentrates on maximizing computing performance, generally while sacrificing console services and more exotic devices (Sound cards, USB, etc.) Server virtualization implementations typically include either RDP or VNC for remote access to a virtual console.
On Linux, your choices for Desktop Virtualization include:
- VMware Workstation -- it's commercial, somewhat expensive, mature, and provides the most hardware, device, and guest OS support of any solution.
- VMware Player -- it's commercial (freeware) and only supports VMs that were created elsewhere. Available with Ubuntu.
- Parallels Workstation -- it's commercial, somewhat expensive, and not up to par with VMware. Doesn't support 64-bit guests.
- VirtualBox -- available in commercial (freeware) and community versions (GPL). Fedora's preferred solution.
On Linux, your choices for Server Virtualization include:
- VMware Server -- it's commercial (freeware), mature, and provides the most hardware, device, and guest OS support of any solution. Available with Ubuntu.
- Xen -- it's open source. A para-virtualization solution, it has only recently added hardware-virtualization, so Windows guest support depends upon specific CPU support.
- Virtual Iron -- a commercialized version of Xen that adds native virtualization.
- KVM -- it's open source. It depends upon QEMU for the last mile. Ubuntu's preferred solution.
- Linux-VServer -- it's open source. It provides virtual jails based on the host OS kernel, so no Windows guests.
For myself, I stick with VMware Workstation (7+ years) and VMware Server for my Linux-hosted virtualization needs. At work, it's VMware Workstation (on Windows), VMware Server (on Windows), and VMware ESX (on bare metal). I'll probably have another look at Xen, KVM, and VirtualBox at some point, but for right now compatibility between work and home is paramount.