1. Gojira/Godzilla (1954)
Japanese theatrical poster
What It’s About: Godzilla terrorizes Tokyo in the midst of a love triangle and scientific sacrifice.
Why It’s Unique: The original, classic Godzilla defined the kaiju genre. It has everything from serious drama to groundbreaking special effects.
Favorite Scene: Godzilla’s breath melts electrical towers that were painstakingly constructed of wax to achieve the effect.
Watch the original trailer here.
2. Mothra vs. Godzilla (1964)
Japanese theatrical poster
American International Pictures falsely advertised Mothra vs. Godzilla for the American release. The poster art is based on an original design by acclaimed artist Reynold Brown.
What It’s About: Mothra and her larvae save Japan from Godzilla, even though, ultimately, greedy businessmen are at fault.
Why It’s Unique: Always a kaiju fan favorite with an excellent Toho kaiju crossover plot. Mothra’s mystical nature is explored, while Godzilla remains a ferocious force.
Favorite Scene: Unique Godzilla reveal as he rises up from underground rather than the ocean. Also, the webs the larvae use to battle Godzilla were an incredible effect for the time, created from liquid Styrofoam.
Watch the original trailer here.
3. Invasion of Astro-Monster (1965)
Japanese theatrical poster
What It’s About: Planet X steals Godzilla and Rodan through trickery and unleashes them on Earth along with King Ghidorah.
Why It’s Unique: Alien invaders become a staple of the series and Godzilla does a famous dance.
Favorite Scene: There are some amazing optical effects of the Xians and their huge flying saucer, but Kumi Mizuno steals the show as Miss Namikawa, convincing Glenn her love is real by saving his life.
Watch the original trailer here.
4. Terror of Mechagodzilla (1975)
Japanese theatrical poster
What It’s About: Cyborg love (spoiler alert) helps Godzilla defeat Titanosaurus and Mechagodzilla.
Why It’s Unique: Last film of the Shōwa series with excellent continuity from the previous Godzilla vs. Mechagodzilla (1974).
Favorite Scene: There’s a beautiful “real sky” shot of Titanosaurus (kaiju were rarely shot outside of a studio), and Mechagodzilla often becomes a giant fireworks display as he blasts his array of weapons all at once.
Watch the original trailer here.
5. Godzilla, Mothra and King Ghidorah: Giant Monsters All-Out Attack (2001)
Japanese theatrical poster
What It’s About: Godzilla is revived by the spirits of World War II Japanese soldiers and can only be stopped by a trio of kaiju guardians.
Why It’s Unique: Mothra, King Ghidorah, and Baragon are “re-cast” as mythical guardians.
Favorite Scene: A terrified woman, helpless in traction, screams as the possessed, white-eyed Godzilla stomps past her hospital room. As she breathes a sigh of relief, Godzilla’s tail swings around to destroy the entire building!
Watch the trailers here.
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Part one of Destroy All Computer Generated Monsters is here.
Movie poster image credits: Wikipedia, Wrong Side of the Art, and Skreeonk
2 Warps to Neptune 
I have to say I would watch any Godzilla movie again at the drop of a hat, so it was difficult to choose five! My choices were a little influenced since I had to get a Kumi Mizuno appearance in there, plus I wanted to be sure the Heisei era was represented.
Mizuno was brilliant (and gorgeous) in Astro-Monster. It’s so rare to hear praise for the human performances in kaiju films outside of the original Godzilla, so I love your choice. Not to mention the fact that Astro-Monster may have the best kaiju performances and effects of the entire series. (The abduction and Planet X sequences are so beautifully done.)
I’ve been rewatching all the Heisei series, and I have to say, I think it’s generally underrated. The English dubs are atrocious, so maybe when we get decent releases, more respect will follow.
There are still a few Godzilla films I haven’t seen in more than 20 years, but if I had to make a list right now it would be almost exactly like yours, except I would include Godzilla vs. Destoroyah in place of Giant Monsters All-Out Attack, and Godzilla vs. Mechagodzilla in place of Terror of Mechagodzilla.
Well done, sir!
I make a point of finding the Japanese language versions by any method necessary! Godzilla vs. Mechagodzilla is fantastic, too – I’m a sucker for the King Caesar song.