Goji pretty much nailed it, so I'll just add my two yen.
1954/56 - Seemed to be like radioactive steam, like might get released from a reactor. Classically, some dragons had no fire, just breath that was hot and fetid, sometimes acidic.
G Raids Again - Seems to be evolving into a beam, still not entirely focused.
Kong/Mothra/Ghidorah - Focusing more, still seems half an impact weapon as much as a burning one. Explodes weakened targets.
Sea Monster/Son/DaM - More and more like a true phaser, even varying in what it does a bit (BTW, the AIP dub of DaM features Hal Linden and George Takei)
Hedorah - Can actually be used as an awkward rocket
Gigan/Megalon - The targets seem harder, so the beam must strike dead-on and point-blank to really do the damage.
MechaG - Power upgrade seems to match the foe involved, so hard to tell
Hanna-Barbera - Laser eyes...just laser eyes. Let's move on.
G84/85/Biollante - Sharper, brighter, more destructive. Several efforts to 'reflect' the beam back at him--the beam is invariably too much. G is firmly established as a walking nuclear reactor.
90's Ghidorah/Mothra/MechaG/Space G/Destroyah - His dorsal fins are often joined by his entire body and the blue-white beam is sometimes overridden by a red-orange beam that has to build up and is completely overwhelming. This version of G finally builds up too much power and implodes.
1998 - In a scene some think was thrown in to placate angry fans, flames appear to leap from the mouth of 'Zilla', though it could also be that the line of flame leapt back to it. In the superior animated series that followed, the grown offspring indeed possessed that weapon.
Millennium/2000/Megaguirus - The red-orange beam is beginning to predominate, and is able to take on pretty much anything it hits.
2001/GMK - G's power levels in this are infamous. He is able to summon a full beam with no effort and no notice, completely incinerate/atomize his foes, and is able to use the beam to sweep the sky of attacking aircraft without a break.
2000's MechaG - Still high by historical standards, but toned down just a bit from 2001.
Final Wars - G surpasses or sinks further than GMK when he attacks an oncoming asteroid that has yet to enter Earth's orbit! Seriously, his beam is now like the Kame-ha-meha from Dragonball Z. A fun movie, but in spots, so very bad.
Well, here's hoping the next revival series learns its lessons from all this.
