The first two movies (Godzilla, GRA/G'85, GvBio) strike a darker and more serious tone that address contemporary fears. The second film adds an opponent (Anguirus in GRA, Biollante in GvBio) and the battle between that opponent and Godzilla will be unusual in comparison to later films. That movie, unfortunately, doesn't do as well as the previous one at the box office and there's a short break before the next film.
The third film (KKvG/GvKG) retools the series into something more lighthearted and fantasy-oriented, dropping the more serious approach of the previous films. It proves to be a big box office success and, as a result, the rest of the series tries to emulate it to some degree.
The fourth film introduces Mothra (MvG/GvM)
From the fifth film forward, Godzilla shifts from strictly a villain protagonist to an anti-hero who battles progressively stranger opponents. Godzilla's son will be introduced during the period after the fourth film but before the halfway point.
About halfway through, the studio produces a film intended to end the series (DAM/GvD). The film is a success, however, and the series continues. Unfortunately, it is immediately followed by a film that represents too large a shift from the norm and some call the worst in this particular series, if not the whole franchise (All Monsters Attack/Zilla'98). This disliked film will prominently feature Godzilla's son in some capacity, after which he's effectively dropped from the rest of the series.
The series then becomes experimental for several films, trying a few different approaches. Some consider this the low point and consider some of these films the worst, others herald it as a resurgence of creativity.
The series finally concludes with a Mechagodzilla duology (GvMG'74, ToMG/GxMG, Tokyo SOS).
Really, the biggest hiccup is Final Wars, which messes things up by including Minilla and being one film past the Mechagodzilla duology. Otherwise...this is surprisingly uncanny!
