Linux is all about freedom and choice and Ubuntu is definitely a large part of it. The default Ubuntu is pretty enough but in case you want to look at alternative environments which improve the eye-candy, read on.
Unity: The New Kid on the Block
Unity is the child of Canonical and Ubuntu and is the default shell of Ubuntu. Unity comes in two variants (2D and 3D) and redefines the way how users can interact with Ubuntu. Trust me, the shell is quite beautiful, the launcher and the dash are pretty sleek too. Unity is supports Compiz (in fact Compiz has a plugin for Unity). Unity supports 'lenses' which are basically ways to search for content (say files, music, applications and so on). Unity is under heavy development and new features are being added to the shell as you read this.
GNOME Shell: Made of Easy
GNOME Shell on Ubuntu is a nothing short of a smart and beautiful looking desktop. It may take some time to get used to GNOME Shell as it completely deviates from the idea of a traditional desktop. A lot of the old GNOME 2 features have been removed and new features have been added. GNOME Shell has can be themed extensively and a huge number of themes are already available. In short, if you want a fast, productive and an ultramodern desktop, you should consider installing GNOME Shell on Ubuntu.
KDE: Eye-candy and Total Freedom
KDE has always been synonymous with eye-candy and KDE 4 does not fail to deliver. While GNOME is known for its simplicity, KDE has a reputation for being extensively customizable. Think about anything on KDE and there is a high change you can tweak it. With smart widgets and bouncing balls on you desktop, KDE has a well organised collection of software that provide you with a consistent user experience. If you are new to Linux and like eye-candy, I'd ask you to try Kubuntu, the KDE spin of Ubuntu.
KDE: Netbook Style
I am a big fan of KDE, not because I use it a lot but because the KDE project as whole never stops to innovate. Every now and then, it churns out new projects and prototypes (which I think is amazing). And with KDE comes total freedom to customize your desktop in any way you want. KDE netbook remix is primarily designed for netbooks but can be used on desktop computers as well. I won't say much but it's nothing short of pure awesomeness. Go KDE!
The Mighty Pantheon
In case you haven't heard about it, Pantheon is a new shell from the Elementary project which is currently under active development. It is not recommended to install Pantheon for production systems as it is not ready yet. I installed the unstable version from a PPA and it was stable enough for me. This shell is an absolute beauty and the nifty application launcher is super cool. Note that the Awoken icon set has been used along with the Ambiance GTK3 theme.
GNOME Classic: Probably the Best
I've started using Linux with GNOME 2 and never had to look back. It is still a desktop environment with blows everything away. The panels are totally customizable, there are many interesting applets for the panels and you can always add a dock or two. If you user Compiz along with it (especially the desktop cube), no other desktop environment of any operating system can match yours. After GNOME moved to GNOME 3 (featuring GNOME-Shell), the project was forked into a new project called Mate.
XFCE: Love it
Initially started as a fork of GNOME 2, XFCE is a light-weight yet fully fledged desktop environment. And contrary to what some people may believe, XFCE can be heavily customized and made to look as pretty as any other desktop environment (the picture shows transparency support in XFCE). You can install XFCE on Ubuntu on use Xubuntu, the XFCE spin of Ubuntu.
LXDE: Lightweight and Awesome
LXDE is another minimalist desktop environment which is aimed to serve lightweight devices and old computers. Personally, I find the stock LXDE to be ok (but not all that pretty). LXDE support Openbox themes and some of them are quite pretty. In fact, Lubuntu has an excellent default look and feel. Check out a couple of good Openbox themes from here.
Badge of Honor: Linux Mint
Linux Mint is one of the best Ubuntu distro which customize Ubuntu largely (they even add non-free codecs). And the result is a lot of eye-candy and goodies packed into one desktop operating system. Trust me, you have to try this one out even if only for its looks.
Build Your Custom Desktop
There is nothing like customizing your desktop to suit your needs. Adding Conky and AWN, Cover Gloobus, globalmenus and launchers, you can create the ultimate desktop. There is no reason not to tweak you desktop, even if you are not an expert. Just play with things and get that perfect desktop done.