Heisei Era
Dwindling box office returns for Godzilla's later entries in the Showa series showed that it was break time. Tomoyuki Tanaka fought hard to get another Godzilla movie off the ground and he finally managed it in 1984. The fruits of his labor erased all of Godzilla's history with the exception of the 1954 original, a wise move in bringing th big guy back to his dark roots.
The Heisei series relied less on cheese and more upon plot (some a little too complicated to comprehend, if they're comprehensive at all) and monster battles became more stiff and laser beam focused, but all eight films put together made for a fun arc nevertheless.
Godzilla 1985 (Gojira, 1984)
Godzilla vs. Biollante (Gojira tai Biorante, 1989)
Godzilla vs. King Ghidorah (Gojira tai Kingu Gidora, 1991)
Godzilla and Mothra: The Battle for Earth (Gojira tai Mosura, 1992)
Godzilla vs. Mechagodzilla (Gojira tai Mekagojira, 1993)
Godzilla vs. SpaceGodzilla (Gojira tai Supesugojira, 1994)
Godzilla vs. Destoroyah (Gojira tai Desutoroia, 1995)