I've found KDE Plasma 5 to be very fast and strong.
KDE also has its own application family. For many years, the apps and the desktop were tied at the hip. You could use other programs with a KDE-based Linux desktop, but at times it wasn't easy. Today, the two are separate.
The other major Linux desktop interface, GNOME, started as a reaction against KDE. Over the years, KDE and GNOME supporters have clashed frequently, but the hostility between the communities has declined over the years.
One reason that conflict cooled down is that GNOME 3 lost a lot of its popularity. People, including yours truly, really hated GNOME 3 when it first came out. Linus Torvalds, Mr. Linux himself, disliked it so much that he called for a GNOME fork in 2011.
That's exactly what happened. There are two major GNOME forks, Cinnamon and MATE, which are covered later in this overview.
GNOME, now up to version 3.12, has corrected many of the problems that early adopters had with it, and has been gaining back some of its fans. You can try it out on Arch Linux, Fedora, or Ubuntu GNOME.
In part, people dislike Unity because it was meant from day one to be a "desktop" environment not just for desktops, but for tablets and smartphones as well. At the time — 2010 — the iPad had just been released, and only Canonical was thinking about coming up with a single interface for multiple devices.
It's not my favorite desktop environment, but it's the best desktop I've ever seen for new users. I mean, if my mother-in-law, who's in her 80s can use Unity, anyone can use it!
If you want to see it for yourself, download Ubuntu 14.04.
The desktop I love the most is Cinnamon. This environment started as a GNOME fork, but it's become much more.
What I like about Cinnamon is that it is, in my mind, a perfect blend of the Windows XP and GNOME 2.x interface. The result is a perfect WIMP (Windows, Icons, Menus, and Pointer). It may be old-fashioned of me, but I still think this is the best desktop interface style. If you don't believe me, consider how many people hate Windows 8's Metro.
The best way to try Cinnamon is with Linux Mint.
The Mint and Ubuntu developers weren't the only ones who liked GNOME 2 but disliked GNOME 3. The MATE programmers decided they would do nothing less than continue GNOME 2 development.
Like Cinnamon, MATE looks a lot like GNOME 2.x. The main differences are under the hood. MATE is designed to work with lower-end hardware than Cinnamon. This makes it a better choice if you're using an older PC.
There are many other Linux desktop environments, besides KDE and the GNOME family. One that I am particularly fond of is LXDE.
I like LXDE because it gives low-powered PCs a lot of traditional desktop goodness. It's also very easy to use.