Do all trains have reserved seats?
Often, trains have some wagons dedicated to reserved seats ('shitei-seki'), whilst others are dedicated to unreserved seats ('jiyu-seki'). This is the case for Shinkansen trains.
However, most local trains don't have reserved seats, whereas other trains like the Narita Express only have reserved seats. (This does not mean that you will need to book in advance but only that, when you buy your ticket, you will be assigned a seat number).
If you are not catching your Shinkansen during peak hours (between 7 am and 9 am and 6 pm-8 pm), and during bank holidays, you do not need to book your seat and you can use any non-reserved seat by showing your Japan Rail Pass.
In fact, the Shinkansen trains run very frequently (every 30 min), particularly on the Tokaido line, between Tokyo and Kyoto, so you don’t have to worry about booking.
However, if you want to book a seat you can do so without additional charges before you catch your train by going into a booking office at the train station (midori no madoguchi) and showing your Japan Rail Pass.
Booking website are usually in Japanese only, and therefore not very easy to use for non Japanese speakers. The JR East Shinkansen Reservation office is the only one with an English version that allows online booking.
However, you can only book Shinkansen and Limited Express trains running on the JR East network, that is to say Tokyo, the Northern part of Japan and the Narita Express.