With so many different derivatives it can be quite difficult to decide which one to download. If you're really anxious to get started, just use standard Ubuntu.
What if I choose the wrong distribution?Edit
The difference between Kubuntu, Xubuntu, etc. is just the software that's installed. Generally, switching to any other variant is fairly trivial and is more like adding more onto the system rather than replacing parts. Once you get one, you can easily mix and match components that are associated with one edition with another.
In short: don't worry about it; you can change your mind. That's one of the things that's great about free software: the freedom.
Ubuntu standard is the most common (and most supported) version of Ubuntu which suits almost every desktop user. It works on most PCs built in the last 3 - 5 years and maybe some older ones. Standard Ubuntu uses the Unity desktop environment by Canonical. (in contrast to KDE or XFCE).
Who should use it? People that just want a simple but powerful desktop operating system, with fairly recent hardware. Both people with and without previous Linux experience should find it easy to use.
A rolling release Linux distro, this modifies Ubuntu to use the GNOME 2 desktop environment, after Ubuntu switched to Unity. Ubuntu 10.x and below users should have easy goings with it.
Kubuntu is the KDE based derivative of Ubuntu. Like standard edition it should be fairly easy for new users to pick up. (For windows users it may be easier than Standard Edition as its UI is more like Windows.) It should work with PCs built in the last 3 - 5 years but older PC's will struggle to run several applications at once.
Who should use it? Like above people that just want a Desktop for their newish computer. Kubuntu would probably be better suited to previous Linux users and Windows users than migrants from Mac.
Xubuntu is an XFCE based derivative. It is designed to run on older and slower hardware and features much more lightweight software than K/Ubuntu. Xubuntu has a very similar interface to Ubuntu Standard Edition and people with no previous Linux experience should find it easy enough to navigate. It should work with PC's built in the last 10 or even 12 years.
Who should use it? People with slower/older computers with aging hardware or people that prefer a lightweight Operating System.
Ubuntu Server EditionEdit
Ubuntu Server Edition is the most advanced version of Ubuntu. By default it comes with a LAMP server but it can also be used for bare command-line only machines or as a starting point to build a customised system. It has low system requirements so should work on computers built in the last 10 years.
Who should use it? Network admins, system administrators, and people with a fair bit of previous experience of Linux and that are not afraid of the command line.
Ubuntu Studio is a media based Ubuntu derivative. It has fairly high system requirements so you will need a recent machine to run it to the best of its ability.
Who should use it? The arty types. People that want to run a music studio, film cutting room or art studio from their new computer.