If you just want an answer for the WGS84 without programming up the algorithm and without paying for the Mapping Toolbox, download the Matlab package Geodesics on an ellipsoid of revolution. This includes an improvement in the Mapping Toolbox function, called geoddistance. To solve your problem
format long;
geoddistance(12.18993,133.45898,14.34243,65.12750)
->
7381566.23351761
The arguments to geoddistance are in degrees and the result is in meters. This does the calculation for the WGS84 ellipsoid. If you want to use a difference ellipsoid specify a 5th argument [a,e] (equatorial radius, eccentricity). (For a sphere, set e = 0; if you want to specify a prolate ellipsoid, set e to a pure imaginary. Accurate answers are returned for |e| < 0.2.)
Incidentally many of the pictures of geodesics shown in the Wikipedia article on ellipsoidal geodesics are drawn with this package.