Martin Fowler in his recent blog post about big screen emphasizes the importance of the workspace size, as in the size of the screen. He says that you cannot see much on a small screen and must switch between windows that overlap each other. I totally agree with him.
I was lucky enough to work at companies that could afford spending a little extra for the benefit of increased productivity. At Siemens I had 21" monitor, which was the biggest you could get at that time. Then at 3D3.com, I had two 17" monitors, which was again an excellent choice (one screen for programming, second screen for running the app/testing).
Fast forward to present, I work at Atlassian and the choices are great. If you work fulltime you can choose between a huge 24" widescreen monitor or TWO 20" widescreen monitors. When I got my 24" monitor, the pair programming just got better.
I use a laptop at home and I used laptops for work at MSC and Agreon. I never had any problems with my eyesight. Except the time when I worked for Agreon and used a Dell laptop. My eyesight got worse and I had to wear glasses at the end of the day as my eyes were strained. Now at Atlassian, with 24" monitor in front of me, I don't need to use my glasses any more. My vision is just fine. (It must've been the screen of that Dell laptop, IBMs and Toshibas are fine) If you use a laptop, at least ask for a stand so you raise the screen to your eye height. A simple bookstand will do as long as it is strong enough. Anyway, laptops are no good for pair programming.
So a big screen is good as you can display more valuable information on the screen. However, one screen still does not save you from application switching. If you are lucky enough to have two screens, you know what I am talking about. It's just a pleasure not to be forced to switch between apps as you can easily have one on one screen and the other on the second screen. A typical scenario is coding and running the (web) application, or coding and reading documentation.
At Atlassian we take turns in support. A developer from each team takes a fortnight turn to join the support team. We usually move to support area (so we can be close to the members of support team). We have a dedicated "support desk", which has all hardware necessary. The only piece missing is the computer that the developer brings along. The monitor on support desk is a 24" widescreen monitor.
When people move to support they bring their own desktop computers. I drag my monitor as well. It's the same 24" monitor and I always think that it'd be a waste to let it sit unused on my "dev" desk for two weeks. I hook it up and voilá! Two 24" widescreen monitors give me the greatest work space I can get (for now). I gotta tell you, it's really fantastic to have these two screens. You can be digging in the code on one screen and doing something else on the other screen. I usually have a virtual machine running on one and a browser in the other. No switching, no overlapping windows.