Does refresh rate matter?
An extremely common misconception is that 'LCDs do not use refresh rates'. This may be true for the most primitive form of an LCD, a Liquid Crystal Module (LCM), but a full-fledged LCD monitor must remain compatible with the refresh rate mechanisms in use by current Cathode Ray Tube (CRT) monitors and VESA standards.
Besides this, many claim that DVI is not capable of transmitting a refresh rate above 60 Hz. It very well is possible to deliver a vertical frequency higher than 60 Hz. The only way LCDs differ when dealing with refresh rates is in their driving electronics. A Digital Signal Processor (DSP) takes the refresh rate and interpolates it to something the TFT driver can receive, which is almost always in the range of 56-64 Hz (generally 60 Hz) according to many datasheets. This doesn't mean that smoother motion won't result from a higher refresh rate. In fact, more fluid motion should be immediately noticeable when running an LCD over its default 60 Hz. If the monitor has a mode higher than 60 Hz in its memory, it won't be damaged by running beyond 60 Hz. Furthermore, many run above 60 Hz when they have Vsync on so that they aren't capped at 60 FPS.
One rare problem is that the overdrive chip lacks a look up table for the refresh rate and thus doesn't function correctly. As far as I know, this is only a problem on the Samsung 970P, where running 75 Hz impairs the overdrive. See here for more details.
So, where are the 120, 180, and 240 Hz LCDs?
On January 7, 2009, Samsung demonstrated the 2233rz at CES, the first monitor capable of true 120 Hz operation. The monitor is now on sale in combo with the NVIDIA 3D Vision package for roughly $600 USD, and very recently has become available standalone for $400 USD. ViewSonic followed up with the VX2265WM, another pioneering monitor that doesn't use interpolation or frame insertion techniques to reach 120 Hz.
As long as we mentioned frame insertion, we should talk about the other ways in which a monitor can be "120 Hz" (or, potentially more). One technique named Black Frame Insertion (BFI) inserts one black frame between each frame at 60 Hz, resulting in an effective 120 Hz. This method causes flickering reminiscent of CRT-based monitors at lower refresh rates, but it does help clear retinal persistence and gives the illusion of smoother motion due to a lower perceived Motion Picture Response Time (MPRT). Often there will be about 16 backlights across the screen that are switched off sequentially from left to right to help reduce overall screen flicker while still providing smoother motion.
Motion Picture Acceleration (MPA), developed by Samsung, is another 120 Hz "faking" method which relies on intercalation (literally, calculating the thing in the middle). Given two frames, intercalation will generate an intermediary frame that combines the geometric aspects of the two adjacent frames. It is a form of temporal antialiasing in a way because it smooths motion over time, not as FSAA (full-screen antialiasing) does with space. To better understand the concept, you can imagine three frames. Frame 1 is a rectangle. Frame 1.5 (the intermediate) is a rounded rectangle. Frame 2 is an ellipse. Do you notice how we gradually morphed the shape into an ellipse through geometric intercalation? We took a property of the ellipse, the rounded exterior, and applied it to the first frame. It is very similar to how Adobe Flash generates intermediate motion given two key frames. See the example below.
