The KTX (Korea Train Express) is Korea's high speed railway. Currently, it only services about a dozen stations in the busiest parts of Korea, but that's good enough for me. (And by the way, check out this map to see all of the new lines in the works.)
We can get to Seoul in under 40 minutes, to Daejeon in 15, and all the way down south to Busan in just over 2 hours. That's some fast traveling. Also, the whole travel environment is significantly nicer than a regular train and light years better than the subway.
Also, they've streamlined their reservation system, so you can reserve tickets online using only your credit card number and passport number. Then, when you get to the station, you can pick up your tickets. (This is much improved over the former system which basically required a DNA sample and a signature in blood.)