Reserve seats in trains

I am using Hyperdia to check trains for my upcoming trip to Japan and I can't help to notice how expensive the seat fee is.

How does that work? Can I just pay the price of the ticket and not pay the seat fee?

It seems logical for me that if I buy a ticket I am allowed to sit or am I mistaken? Is this only for certain cars in the train that have reserved seats?

Thank you for any clarification

I am using Hyperdia to check trains for my upcoming trip to Japan and I can't help to notice how expensive the seat fee is.
How does that work?

Unfortunately hyperdia lists supplement fees in a confusing way and rolls mandatory limited express fees in with option reservation fees, green car fees and so on. But generally speaking, if there is a seat fee listed then it is mandatory.

It seems logical for me that if I buy a ticket I am allowed to sit or am I mistaken?

You may sit in unreserved cars with free seats, or in reserved cars with a seat reservation.

Is this only for certain cars in the train that have reserved seats?

yes

See here for more info:

http://www.japan-guide.com/e/e2323.html
http://www.japan-guide.com/e/e2016.html

Here is supplement information you might want to read:
http://www.jrpass.com/forum/topics/general-japan-travel/posts/what-is-...

It seems logical for me that if I buy a ticket I am allowed to sit or am I mistaken?

If you pay only the basic fare from point A to point B, then you are allowed to go from A to B using local trains (and yes, you are allowed to sit ;) ). If you want to use a limited express or a Shinkansen, however, you have to pay additional fees since you get a higher level of service. It is those additional fees to which Hyperdia refers by the very poorly chosen term "seat fee".

"Seat Fee" is a bad term by HyperDia for additional charges on railroad services.

A JR Express / Limited Express / Shinkansen charge is required even if you cannot sit on a seat (due to crowdedness during a New Year season, for example) when you have a ride without seat reservation.
This JR charge becomes a little higher when you reserve an Ordinary-Class seat, or becomes pretty much higher when you reserve a Green Car seat.
(Also some non-JR higher-speed train services require an additional charge.)
JR Local trains can be taken if you just pay the basic fare. The same applies, in most cases, to JR rapid trains.

When you use a railroad service requiring an additional charge, usually your tickets are issued separately concerning the basic fare and for that railroad service.
e.g.
When you have JR rides from Tokyo to Nara within 4 calendar days, and take first a Rapid train (instead of a Shinkansen train) to Odawara, then a Shinkansen train (without seat reservation) until Kyoto and then a Miyakoji Rapid train to Nara, you get issued
a basic-fare ticket to travel from Tokyo to Nara (in exchange for 8750 yen as a basic fare)
and a Shinkansen ticket for a non-reservation ride from Odawara to Kyoto (in exchange for 4540 yen as a Shinkansen charge).

If you travel with a JR (short-distance) basic-fare ticket which can be valid for one day only, the ticket expires when you get out via an exit gate of a station.
With a JR (long-distance) basic-fare ticket which can be valid for plural days, you can get out via an exit gate of a station on the way and resume your rides from that station, but you cannot turn back or skip a part of the route.

A route-finding tool (such as HyperDia or Jorudan) is not designed to show the total railroad cost on a JR long-distance leg along which you get out via an exit gate in one or plural stations.
A total railroad cost on a leg is not always equal to a sum of costs on its parts.

Among transportation passes, some cover only basic fares, some fully cover both basic fares and higher-speed service charges, or some cover higher-speed service charges only for certain trains.