Originally Posted by RichardInSF
There are so many shinkansen that unless it is a public holiday in Japan there is no need to purchase in advance -- just buy the ticket when you're ready to go.
Which unfortunately, it is. August 13 to 18 is right smack dab in the middle of the traditional Obon summer holidays (the week centered around Aug. 15th). Companies go on holiday for about a week, and much of Japan rides the trains and planes to hometowns and other places around Japan on vacation.
Seats on both trains and planes sell out quickly. By coincidence, the Japanese TV news reported today that Japanese are traveling domestically more than ever, and that seats on trains and planes for the approaching Golden Week holidays (April 29th to May 5th) are, for the most part, already sold out.
In a nutshell, whether you go to Kyoto by plane or train, I would make sure I had firm reservations in hand.