Most LCDs have zero flicker. The only exception I've come across are super high-end LCDs with calibrated auto-tracking backlights, where the backlight is controlled with PWM, and where the PWM frequency is too low - unfortunately, we have these at work, the backlight PWM brightness control (not the inverter PWM) is driven at about 200 Hz and it drives me spare, as I see flickery trails every time I focus on a new point (a significant problem when you have 2 or 4 20" screens in front of you). Again, this is manufacturer specific - I've found this to be a problem with Barco monitors, but Eizo use a much higher frequency brightness control PWM, and I'm fine with them.
Low end LCDs do have a 'shimmering' effect - this is the result of dithering (usually called FRC), and is sometimes referred to as 'screen door' effect. Most LCDs screens only have 6 bit digital-to-analog converters in them, so in order to display more than 262k colors, they rapidly switch pixels from one color to another, to try to create an intermediate one. The result is a effect like subtle 'snowstorm' bad reception on old analog TVs. A lot of people seem to perceive this as flicker, even though it isn't really flickering. This isn't a problem with high-end panels that offer true 16.7 million colors.
I've just got a new HP LP2475W, and it's absolutely perfect. Not a hint of flicker or shimmer. Absolutely rock steady picture - no eye strain whatsoever - and, believe me, I'm picky.
One problem that people have with LCDs, especially when new, is that the backlight is extremely bright. The factory settings on my HP were intolerably bright - only after reducing the brightness control to 0, did I get a comfortable level. I suspect that as the back light ages and beds in, the excess brightness will fade, and I'll be able to adjust the brightness up to a stable setting.