I've used a fair smattering of virtual hosts and hypervisors both at work and personally. So here's what I think of them all (the free ones, anyway);
VMware: Probably one of the easiest to get set up and master. Dead simple point-and-click interface. Learning this is good if you want a career in virtualization because it is the yardstick by which all others are judged. There are a lot of features though that are disabled in the free version that are used in corporate environments... but you'll have the basics down.
Hyper-V: Also very simple to use and manage... but unlike VMware means you can run it as a side-piece on your existing Windows box rather than having a dedicated piece of hardware just for virtualization. Already built into most modern Windows variants, and used somewhat regularly in corporate environments. Again, paid adds features and support.
Citrix XenServer: Takes the basics of the open source Xen and adds a pretty damned nice GUI. Paid version adds support, but most of the major features are available and functional in the freebie. Trial versions of everything are available. Memory management out of the box is a bit of a pain (no overcommitment by default) but easy enough to modify. Use in corporate environments tends to follow people who have significant Citrix/XenDesktop infrastructure.
Xen (Open Source): By far the best to learn EVERYTHING about how virtualization actually works, but probably the worst for actually getting running VM's. There are GUI tools to simplify it, but since Xen is currently moving to a new toolset that is incompatible with most GUI interfaces, and the GUIs tend to be a smidge buggy on occasion it's usually easier just to learn the command line. Of course, then there are config files, XML files, bridged network interfaces. If you want to learn about the internals this is the way to go... but if you're only going to dedicate a day to trying each one then you might want to skip it... this one will take a couple of days at least even with the several well-written HOWTO's. Having said that, once everything is working it's really nice and you can turn around and say that you know how virtualization works, instead of just saying you know how a single product works!
VirtualBox: Like VMware is good for the beginner to learn the basics because it does have a nice GUI that guides you through everything. Update notifications are a constant irritant though; it seems that every week they're releasing an update for this bug or another... I turn that off and upgrade when I feel like it! However, use in corporate environments is almost non-existent. Good support for most OS's, and decent support for 3D graphics and the like but still pretty kludgy. I use it on my Mac for running my BootCamp partition while under OSX... mostly so I can access stuff on that installation and run updates and the like without having to reboot OSX.
I broke out the two main versions of Xen because they are significantly different. They are similar at the core (based on the same code) but Citrix has it own front-end tools that are incompatible with the tools you'll use under open source. However, the commands are the same and so learning open source Xen will have some bearing on using Citrix Xen.
Of course, there are plenty of other hypervisors out there. My personal recommendation if you just want to play would probably be Hyper-V or VirtualBox. VirtualBox has the advantage of being cross-platform; I don't know if you run Linux or Windows (or OSX) at home, and obviously Hyper-V is Windows only. If you really want to learn virtualization and how it works, then open source Xen is the way to go... I run it on my Ubuntu 12.04LTS box and love it... but it's not for the faint of heart! Setting up the networking alone can be "fun" and you should definitely familiarize yourself intimately with how to undo what you have done so you don't break anything! VMware like I said is used extensively in corporate environments... so if you want to pursue it as a career I'd recommend dedicating a box to an ESXi server and just play with it. It's free and easy... but really doesn't teach much in my opinion.