Though I was fortunate enough to play with a model railway in my formative years, it wasn't until I first visited Japan that I really understood the appeal of "train spotting". Back in the UK, it's seen as a pastime for people with perhaps not the best social skills, often wearing anoraks, photographing trains and discussing subtle differences in locomotive design with each other, rather than participating in "normal" conversation.
But, what is "normal"? There's nothing wrong with discussing topics with like-minded people. In fact, it's very enjoyable. There's not much more boring than banal conversation. I am a camera, computer, mobile phone, shoe, timepiece, anime, music... geek. I'm guilty of finding something interesting, and then going crazy on the topic, finding out everything I can.
Anyway, the "bullet train", or shinkansen, is something that any visitor to Japan should try at least once. If going between Kyoto and Tokyo, you'll want the Tokaido (Way of the Eastern Sea) shinkansen. If you've got a Japan Rail pass (recommended!), you can take kodama and hikari trains, not the faster Nozomi. The speed is actually the same (same trains, too), but the number of stops is different. We took the Nozomi, as there's no point in taking the slower train unless you have to stop elsewhere.
My second tip, is to try to get a seat on the right hand side if going towards Kyoto, and on the left if going towards Tokyo. This way, you'll have a fighting chance of catching Mt. Fuji, in between the never-ending sprawl of housing, factories, and power lines.