VMware is not open-source, and is pretty expensive if you need more than the basics. However it's well-supported in most circles, and its paid-license-support gets it past the PHB hurdle.
Xen is a beast. The time investment alone to get it to work puts it out of reach for even mid-level Linux admins. Plus it requires extra help to run non-Xen guest OSes.
OpenVZ isn't real virtualization. It's OS-level containment and pseudo-virtualization, which can be good for some things.
KVM has real steam behind it. It's already in the mainline kernel, it supports real virtualization (I've been able to get all modern Linux distros running as KVM guests as well as WinXP - WIn8 preview), but can get almost as fast as Xen's para-virtualization with some guest-OS drivers installed. There have been new features added to the Linux kernel to help it (Kernel Same-page Merging is one example). It's not that difficult to get working, especially if you use something like libVirt to do the heavy lifting for you.
I'm not an Ubuntu user, so I can't give first-hand experience using KVM on LTS, but a quick google search turned up this this HOWTOforge article on the latest LTS and from my reading, it seems pretty straight forward.