How many flights follow the North Atlantic Track relative to those that don't?
According to ICAO NAT doc 007 (North Atlantic Operations and Airspace Manual, edition 2014/2015) (PDF), approximately half of the North Atlantic (NAT) flight use the Oceanic Track System (OTS).


  2.1.3: It should be appreciated, however, that use of OTS tracks is not
  mandatory. Currently about half of NAT flights utilise the OTS.
  Aircraft may fly on random routes which remain clear of the OTS or may
  fly on any route that joins or leaves an outer track of the OTS. There
  is also nothing to prevent an operator from planning a route which
  crosses the OTS. However, in this case, operators must be aware that
  whilst ATC will make every effort to clear random traffic across the
  OTS at published levels, re-routes or significant changes in flight
  level from those planned are very likely to be necessary during most
  of the OTS traffic periods.


Note that not all flights in the NAT do cross the Atlantic from East to West or vice versa. For example:


Flights from Northern Europe to Spain / Canaries / Portugal and v.v.
Flights from Portugal to the Azores and v.v.
Flights from Iceland


And then there are a number of fixed routes that allow aircraft that do no meet the minimum navigation performance requirements to cross the ocean. These tracks do not change with the daily winds like the OTS tracks. 



All these are included in the 'about half'

But especially in the Northern part of the NAT airspace, covered by the Reykjavik FIR there are many random routes. According to the website of Iceavia: 


  In 2010, 92.3% of the traffic in the Reykjavik CTA was on random
  tracks and 7.7% was on the NAT tracks.


But that is mainly because the OTS tracks are usual south of the Reykjavik FIR. 

That same page says:


  In effect, where the preferred track lies within the geographical
  limits of the OTS, the operator is obliged to choose an OTS track or
  fly above or below the system. Where the preferred track lies clear of
  the OTS, the operator is free to fly it by nominating a random track.
  Trans-Atlantic tracks, therefore, fall into three categories: OTS,
  Random or Fixed.