Lower response time = less ghosting = less artifacts on screen.
When playing a fast paced FPS or viewing fast-paced sports on TV you will notice a "blur" around moving elements on TV's with high response time.
As for the "gaming mode" from my personal experience it just changes the response time on Samsung TV's to be lower, (also some minor changes in sound and color - possibly a worse (read: quicker) scaler method is used aswell), in does not make much of a difference, nothing infact from what i could see on screen performance wise, and its definately not something you "have to have" as a gamer.
Actually you're talking about two different things. Ghosting is something i havent seen on an LCD in years. Basically ghosting was initially used to describe the phenomena of an image or frame staying on the screen that had passed. Exactly like a burn in except with no lasting effects.
What you're talking about is image streaking where the pixels arent updating fast enough and leave literal streaks, outlines if you will, of fast moving objects. Easiest way this is noticed is when someone fires something like a rocket that is visable across your screen and you can see the path of the rocket trailing behind it when you shouldnt be able to. Or when you're moving down a corridor and you hit a lighted area and the lights bleed into the solid dark wall or floor.
Ghost is all but eliminated, and has been on most quality sets as well as monitors for the last few years. Streaking itself has been pretty much solved over the last couple of years. Basically a set with a response time of anywhere from 8-16ms isnt going to be streaking as long as the manufacturer hasnt lied. You'll have better odds with a Panasonic or Sony set with a 16ms response time then you will with some no-name set thats listing a 12ms response time.
LCD quality very much differs from manufacturer to manufacturer, so its not correct really to tell someone that if a set is 16ms white to black responce time, they're going to see streaking. Most sets list the grey to grey anyway since its more impressive. When buying a modern set, i think its safe to say that both these problems are basically worry free, and you should instead be looking at budget and the other pluses and minuses of the technologies.
The same goes for black levels.
DLPs are best for viewing at distance, you dont really want to use them sitting right in front of them as the picture loses clarity. Its the nature of the beast. They also have bulbs which can be a negative only when they have to be replaced (bulb life has greatly improved) and some do still have sync problems between the picture and the sound but im quite sure thats all but eliminated. DLP technology are also generally reserved for larger screens and likewise look best on larger screens, meaning you dont look at DLPs if you plan on getting something around 40" or less.
Plasmas suck down loads of power, can burn in, but look the best at all screen sizes, but the picture loses quality as well in a room that gets a lot of light and also cost the most. Generally it has excellent viewing angles.
LCDs are usually the best bang for buck. They have great picture quality in well lit rooms as well as dark rooms, they have fast enough responce times to please gamers (as mentioned) and generally dont cost an arm and a leg for a preferred size. Alot of people mention black levels as being a negative, so its really important to pay close attention to this when viewing demo sets or reading reviews because black levels do differ across manufacturers. Sets like the 2006 Panasonic 32" LCDs are generally regarded as having great black levels. We're a far cry from the "MY BLACK IS GREY!" problems of old with most sets these days. The biggest negatives of LCDs in my opinion is they still tend to wash out at wide angles and are still best viewed dead on and the cheaper sets have backlight bleeding which gives people the perception that the set (and thus all LCDs) cant display blacks.
Infact backlight bleeding is the number one cause for people being so bold in saying LCDs have bad blacks or cant display true blacks, which isnt true.
