Here's my list of the most important of the Ubuntu-based distributions.
Kubuntu 10.04. Like the name suggests, the big difference between Ubuntu and Kubuntu is that the K-Ubuntu runs KDE 4.4.2 instead of GNOME 2.30 for its desktop. But Kubuntu isn't just Ubuntu with KDE. Instead of KDE's default Konqueror Web browser, Kubuntu defaults to using Firefox 3.6.3.
Kubuntu also does a nice job of integrating GNOME applications into the KDE 4.4 interface. That's the good news; the bad news is, instead of using a KDE frontend to Ubuntu's outstanding Ubuntu Software Center, you're stuck with the far less attractive and more difficult to use KPackageKit to add new programs and update your software. KPackageKit is fine for experienced Linux users, but Linux newcomers, which is what Ubuntu wants, will find it less than appealing. For more on Kubuntu, check out this excellent review.
Edubuntu 10.04 is the educational version of Ubuntu. It's meant to fill the computing needs of children, students, parents, teachers and schools. As you might guess, it includes easy access to a lot of educational software.
The biggest difference between Edubuntu and Ubuntu is its support for LTSP (Linux Terminal Server Project). This is a server-based program that lets you run Ubuntu instances on thin clients or low-powered desktops. This makes Edubuntu ideal for schools that can't afford newer PCs or system administrators to coddle many individual PCs.
Xubuntu 10.04 is the Ubuntu for people who prefer the lightweight Xfce 4.6 desktop. This is more of a matter of taste than anything else since Xfce is based on GNOME's underlying GTK+. But Xubuntu does have the advantage of being able to run on very minimal hardware. For example, Ubuntu feels a bit cramped on older PCs with a mere 512MBs of RAM, but Xubuntu can run just fine on computers with that little RAM.
Ubuntu Studio 10.04. On the other side of the minimalist Xubuntu, you'll find Ubuntu Studio 10.04, which is designed for multimedia creators and editors. For this GNOME-based version, you'll need all the RAM you can get.
In Ubuntu Studio, you'll find audio tools like Ardour 2; graphic programs such as GIMP, Inkscape and Blender; and video editing software including Blender, Kino and Stopmotion. Consider this the Linux and open-source answer to Windows plus Adobe Creative Suite 5, for a price of free instead of well over a grand, and you'd get the idea.
Those are all the 'official' Ubuntu distributions. There are many other Linux distributions that are based on Ubuntu. These Linuxes, however, while based on the Ubuntu code base, have no official connection with Canonical, the company that backs Ubuntu.
That said, many of these distributions are excellent in their own right. My personal favorite is Mint. Mint, which is quite popular, comes ready to roll with built-in support for proprietary multimedia codecs and hardware. While this can drive free-software purists mad, I think it's very handy myself.
But if proprietary software and drivers give you hives and you want a Ubuntu with no trace of proprietary software, there's a distribution for you: gNewSense. Neither Mint not gNewSense is currently using the Ubuntu 10.04 source for their shipping distributions at this time. Both will be using in though in the near future.
So there you go: an Ubuntu Linux for all seasons and users. Enjoy!