Are unreserved offered on all trains?

I am trying to get an estimate for what all rail travel will cost me over my week stay and have found this site to be very helpful: http://www.hyperdia.com/en/

In using it though I keep seeing "seat fees" and the option to show pricing for reserved seats. I understand the difference in the reserved/non-reserved (and that all seats may be full,) but are unreserved seats offered on all trains? On the hyperdia website, it looks like some trains do not offer unreserved seats (for example: NARITA INTERNATIONAL AIRPORT 1 to SHINJUKU).

Very few trains are all reserved seating. The N'EX is one of them, along with the Hayate and Komachi Shinkansen. Other than maybe a few night trains, i can't think of any others, but you will find the info on Hyperdia.