Several weeks ago I finally made the switch to LCD flat-panel monitors, both at home and at work. Within a week my eyes were doing worse, almost to the point where it was a constant distraction. It's a little hard to understand because even though I used pretty high-quality CRTs with high refresh rates, the LCDs still look significantly better. I took a few steps that reduced my eye strain significantly.
I reduced the contrast. At work my LCD was turned up as bright as it would go, so I reduced the brightness and contrast to just above the point that I thought it was too dark. At home I like to work most of the time without much light in the room, so even though the LCD brightness wasn't cranked way up, it still had a lot of contrast with the rest of the room. So now I try to work with a light on in the room. I'm looking for a small, cool light to put behind my monitor to reduce the contrast with the background.
I also switched my primary text editor, Vim, to a white on black color scheme instead of black on white. I was already using similar white/green/grey on black for all my terminals, 3270 sessions, Windows consoles, etc., but I spend at least half my day staring at Vim. Maybe I need to look at some of the web apps where I spend a lot of time, like Jira, and swap the color scheme on those.
Between those two changes, my eyes feel a lot better now, even though I had to spend even more time working lately.