One of the faculty member of my University told me about Jorudan TrainRouteFinder. It is a English net version of the 乗換案愛 I have on my PDA.
 
The PDA version displayed information between two stations (from anywhere in Japan to anywhere in Japan), such as what train company to use and where to switch trains, and sorts several possible routes according to price, length of trip and easiness. The above net version includes departure and arrival times and much more accurate price information, and it includes domestic flight and bus routes to compare with.
 
If you're not familiar with geography of Japan but would like to try it out just in case, you can enter a trip from a Tokyo metro station Minowa (where Tokyo's cheapest accommodations can be found) to Kitanohakubaicho, which is the closest station (that I know of) to Kinkakuji temple in Kyoto.
 
The software on my PDA is sweet (since it works without net connection), but I wish I could upgrade it to this net service! I particularly missed the bus route information.

Indeed, this is very cool. I ought to get one of those PDA as well for this.

Quote from Hokousha on Sep 30^th, 2006, 9:02am:

This is true. I never used trains between Kyoto and Tokyo. I always used Dream Line Highway Bus, because it's always cheaper. It takes longer, but a night route (sometimes as low as 4000 JPY) saves the price of a hotel room and one can start the day at destination early on. Great for a sightseeing backpacker.
 
I mostly used the PDA software in local transit, where the apparently easy route on the maps can be actually quite a difficult one. There seems to be lots of WLAN hotspots on subway stations in Tokyo, so with hardware one can use either software.