My personal preference is for a well adjusted CRT. At work I have a 17" Dell LCD, which when new to me, instantly gave me headaches and eye strain. The fix, as several above mentioned, was to turn the brightness down, way down in my case. Now it's ok, though I still find a CRT fatigues me less, and to me video looks much more realistic on a CRT.
By well adjusted CRT, I mean to have it not too bright and have it in focus. I have yet to have a CRT with a front panel focus control that works properly. Which means adjusting the one or two focus controls on the flyback transformer (25000 or so volts..). I modded the case and internal shield on my Samsung 900IFT CRT so I can tweak the focus controls without removing the case. This has to be done once or twice a year as the monitor ages. The plus side is, the image is sharper than when new, and with a .2 MM dot pitch, is pretty sharp!
Additionally there is usually a "picture" control on the flyback, which is essentially a brightness control, and can be use to correct the range of the front panel controls (like if the monitor is too dim or too bright, with the front controls at the extent of their range).
With so many volts available to fry yourself with, be very careful and use a plastic TV alignment tool (search 479PR004 at Technitool) when tweaking the flyback. Keep one hand in your pocket and wear rubber soled shoes. Don't ground yourself.. DON'T use a metal screwdriver, even one with a plastic handle...