This is probably the biggest and most common misconception I see on here, so it's going first. Most people are under the impression that the response time is a measure of the display's latency. That ingame feeling of delay between hitting a button and seeing your command play out onscreen, "controller lag" as some people call it. A perfectly reasonable assumption, the value for response time is even given in milliseconds after all. But alas, this delay is NOT what response time measures. Response time is something ENTIRELY different, it just happens to be confusingly named. That "controller lag", delay, latency, whatever you want to call it, is called input lag, and unfortunately it is never listed in the specs of a monitor. You'll need to look to review sites like TFTCentral which actually test input lag using advanced equipment.

Response time, in case you were wondering, is the time it takes for a pixel to switch from one color to another. Typically 1-10ms, it isn't nearly enough to have any kind impact on the perceived latency or "controller lag", especially considering the color transition doesn't even have to be fully completed for us to see and begin reacting to the new image that is being formed. What it can do is cause blurriness in scenes with fast moving objects on high contrast backgrounds. These moving objects might leave a visible "trail" behind them on displays with a very very slow response time. This is called "ghosting" (not to be confused with the smearing/echo effect over VGA connections also called "ghosting"). You can call it motion blur if you like, but that is technically incorrect as the term motion blur usually refers to the "built-in" blur that is part of the content being viewed (movies, etc.). When you pause and the entire scene is blurry, that is motion blur. That blurry image is exactly what the monitor is being instructed to display, and a faster response time won't make it any less blurry.

It's also worth noting that response time is not a single number. Response time is actually a whole range of values, and the specific response time of a color transition depends on which two colors are involved. When a display has a "5ms response time", that doesn't mean it takes 5 milliseconds to switch between any two colors. It means it takes 5 milliseconds to switch between those two specific colors that the manufacturer chose for the test. Of course, since they don't publish which colors are used for the tests, or their testing methodology, or their testing equipment, it does make the number rather meaningless. There is also no standard for which color to use, so not only do you not know which colors are tested, you don't even have the comfort of knowing that all the manufacturers are at least testing the same transitions, whichever they may be. Different display manufacturers can all be testing the response times of different color transitions, which means response time numbers are not directly comparable between monitors. An 8ms monitor can be faster than a 5ms monitor in reality, or a 5ms monitor might be slower than a different 5ms monitor. In the end it hardly matters anyway, since ghosting hasn't been a big problem since the old days of early IPS panels without modern response time compensation technologies, whose response times reached up to 50ms and beyond. With any half-decent modern display, even ones with the infamously slow "IPS" type panels, you'll find that they aren't actually slow at all and that severe ghosting issues are a thing of the past.