First, let me say that I did not go out of my way to put together a multiple monitor setup, but it just happened.
My setup started with one monitor and one computer. The Asus monitor was all by itself for a while. However, we decided to put a flat screen HDTV in the living room and moved an old Sony HDTV into the bedroom. As a result, I ended up with an extra older 42 inch HDTV that I had in the bedroom that I could sell or put in a different room. Since I liked the idea of putting it in my office for various reasons, it found itself on my desk while I decided where to place it. It is funny because someone has mentioned that the TV wasn't very good, but my response was that it wouldn't be in my office if it was the best TV in the house. It was one of the first TV's that had a 1080p input via HDMI, so I am still happy with it. Most of my movie watching takes place in my living room, so this is just a secondary setup.
During the same period, I decided I wanted a better monitor than the Asus for photography and decided to get a refurbished iMac that I could use as a monitor for a MBP via thunderbolt, but also get the full benefit of a great computer. When I got the iMac, I decided to mount the TV over it and the three monitor setup was born.
The main reason I kept the Asus display was because it has numerous inputs, so I can use it with more than one computer. It connects to the iMac as a monitor extension, it connects to an older Windows PC, and it connects to a Mac mini. It is also connected to a receiver, so I can watch AppleTV or the PS3 on it. I have an HDMI splitter, so I can watch the same video signal on the Asus or the Westinghouse HDTV.
I often use the Mac Mini for music while using the iMac for more intensive stuff. The mini also feeds my living room setup, so I don't just use it in my office.
While the Westinghouse gets the least amount of use, I do use it for gaming and watching movies/Directv. My chair is similar to a recliner, so I can lean back with my feet up on the desk and comfortably view it, even though it is mounted fairly high.
So, my answer to "Why have a three monitor setup?" is "Why not?" . It gives the space a lot more functionality, allows multitasking, and saves me from taking a huge hit from selling the displays on eBay as they were replaced. Also, why throw them out if I can still use them?
I don't always use all three monitors, but I have gotten used to having two monitors on most of the time. I use a program called teleport to move one keyboard and mouse from one computer/monitor to another, so it makes for seamless blending of two computers or monitors.