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The Blue Öyster Cult Godzilla theme they used in Godzilla vs. the Thing,hands down best

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5- Legendary Godzilla theme

4- Terror of Mecha Godzilla (Godzilla march)

3- Always 2 Godzilla theme

2- Persecution of the Masses 

1- Godzilla vs. Biollante (Godzilla march)

How can nobody mention Who Will Know from Shin Gojira?

Oh man. Music discussions are always the most difficult for me. I own and have studied all of the soundtracks so thoroughly and yet the music from the Godzilla series is so masterful there's still things about it that I miss. I suppose in order of release these are the ones that stick out the most for me.

- Ifukube's Godzilla's Theme (Mothra vs. Godzilla ver.)
Probably the definitive Godzilla theme of the 1960s. This is an update of the full theme from King Kong vs. Godzilla and the improvements Ifukube made was massive. The A motif at the beginning would define Godzilla for the rest of his career, whereas the B motif (at 0:56) is a variation of Godzilla's theme from the 1954 movie. There's an undeniable sense of depression and tragedy to it, but before it pulls you down to far the C motif's beat begins. It opens with a variation of the popular A motif (1:40), then quickly morphs in to its own thing by 1:54.

The incredible C motif wouldn't come back to the series until 1993's Godzilla vs. MechaGodzilla II. (Or if you want to count stock music, 1972's Godzilla vs. Gigan.) Unfortunately, in 1993 Ifukube decided not to introduce the C motif with the variation of the A motif from Mothra vs. Godzilla. And 1993's B motif isn't nearly as tragic by comparison. In the following 1960s films Ifukube made the B motif more action packed and less emotional, likely due to the shift in tone.

- Ifukube's Godzilla Theme (Godzilla vs. King Ghidorah ver.)
This is an obvious one, but it's just so good. After all of these years I've yet to tire from what is essentially the main template for the Heisei Godzilla's theme.

The first thing to note about this is it's the first Ifukube Godzilla theme recorded in stereo for a film. Sure we've heard stereo updates of Ifukube's work before now, but having the master behind the wheel proves to be a completely different ballgame. His work is far stronger than previous imitations.

The theme is brilliantly pieced together with the popular A motif from Mothra vs. Godzilla opening the charge. After that a new lead-in crescendos into the 1954 Godzilla march. (Though the 1954 march was not initially supposed to underscore Godzilla, the theme had since become synonymous with the character. Thus, Ifukube began using it as Godzilla's theme more consciously by Terror of MechaGodzilla.)

- Otani's Godzilla Theme
I was already a massive fan of Otani from Gundam Wing, Outlaw Star and the Gamera Trilogy. So in 2001 when I found out that he would be scoring Godzilla it felt like a dream come true.

Otani knows how to use electronics without bringing much attention to it, yet scores complex pieces that are often pieced together for visuals instead of characters, ala Ifukube. But here he has a lot of focus on the Godzilla character, much like he did for the first time he scored Gamera.

Instead of breaking up his theme into separate motif's Godzilla's theme is a pulsing, Jaws-like repetition with a sweeping orchestral motif layered on top. As hauntingly action-packed as it sounds, there's also something strangely beautiful to it.

- Oshima's Godzilla Theme
Used in all three of Masaaki Tezuka's films, (Godzilla x Megaguirus, Godzilla x MechaGodzilla, Godzilla: Tokyo SOS) Oshima's theme didn't go through many variations, but plenty of arrangements--She didn't need to change much. It's still the most perfect theme for Godzilla since Ifukube.

The theme opens with pounding war drums that underline its A motif. The B motif blows off the doors at 1:25, being a perfect fit for the character.

My favorite variation is the one from Tokyo SOS. Whereas the pounding war drums were too quiet in Godzilla x Megaguirus and too loud in Godzilla x MechaGodzilla (due to being recorded by the Moscow's International Symphony Orchestra), Oshima struck the perfect balance in Tokyo SOS, where she also played with the way the drums introduce the theme more. The JSXDF theme can also be heard briefly at 2:11 before being swamped by Godzilla's theme (B motif) at 2:49.

The Blue Oyster Cult song was not used in any Godzilla movie-- Especially Godzilla vs. The Thing since that song came out 13 years later.

^No Who Will Know? It was so good that GG used it in a dinosaur story

Who Will Know is a fantastic piece, but I do not classify it as a Godzilla "theme". A theme is usually a piece of music with reoccurring motifs throughout the movie. Who Will Know is only played once with no variation. It merely seems to underscore the scene and Godzilla in that particular moment, not the character throughout.

^Oh ok

Jeez I forgot about Oshima's Godzilla theme, I really like her version of Godzilla's theme a lot.

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Ultrazero,
If I could transplant any Godzilla theme over to the Monsterverse, it would probably be hers.

So people have an idea of what theme is in which movie, I highly recommend plowing through this. It features Godzilla's specific theme from each film:

60 Years of Godzilla's Theme

^It would be cool to see her theme in Godzilla: King of the Monsters

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I also like the Legendary theme

My favorite version of Godzilla's theme will always be the Mothra vs. Godzilla version. I'm not, nor will I ever be, an expert in music or film composition, but I cannot deny the genius of this theme. Not only is it probably the most powerful version of Godzilla's theme, but Ifukube uses it in such a versatile way. The theme works to both underscore Godzilla's rampages and the JSDF's counterattacks against him. It exudes fear, tragedy and excitement, each in a different part of the same composition. My absolute favorite use of this theme is in the opening sequence though. This time, it's played much slower in tempo, and is incredibly ominous and foreboding. By the end, it fades into an instrumental version of "Mahara Mosura," perfectly underscoring the entire opening sequence.

It's hard for me to give any order to the other various Godzilla themes, as the Mothra vs. Godzilla version is by far my favorite. Here are my next four favorite, in no particular order:

Michiru Oshima's Godzilla theme. No other composer besides Ifukube has really come so close to crafting such a unique and iconic theme befitting the King of the Monsters. It is both ominous and exciting, and is in my mind the definitive Godzilla theme for the Millennium series. I enjoy the faster-paced rendition of the theme from Godzilla vs. Megaguirus, but I have to concur with GMan that the theme's use in Tokyo S.O.S. is probably the most effective and incredible to listen to.

The combination of Koichi Sugiyama's "Godzilla 1989" suite and Akira Ifukube's "Godzilla vs. The Tank Corps" and "Godzilla Title" in Godzilla vs. Biollante. One common criticism of the score for Godzilla vs. Biollante is its inconsistency, and how it generally can be all over the place in terms of tone or style. For the most part,  I consider this one of its strengths, or at least a major factor contributing to my enjoyment of it. In this film, Godzilla is not underscored by a single theme, but three, all of which work in how they are used. The first is the original "Godzilla 1989" suite composed by Sugiyama. This theme is often associated more with Biollante, due to its heavy use during her battles with Godzilla, but it is a fitting Godzilla theme. It starts out high-pitched and horrific, then builds up and down through frantic action-packed segments and quieter ominous segments. Used in addition to this are the OSTINATO re-recordings of "Godzilla vs. The Tank Corps" (a.k.a. Godzilla's theme from Mothra vs. Godzilla) and "Godzilla Title" (the main theme from the 1954 film, itself not intended to underscore Godzilla). These themes are varied throughout to underscore Godzilla, in my opinion with great success. "Godzilla vs. the Tank Corps" is as I previously mentioned my favorite Godzilla theme, and is fantastic for underscoring Godzilla's rampages. Only the first two motifs are used, but the theme is still excellently used. "Godzilla Title" is very fast-paced and exciting, and is used to underscore Godzilla rising from Mt. Mihara and his final confrontation with the JSDF at Wakasa Bay. Despite not originally being intended as Godzilla's theme, it works very well in this instance and is a highlight of the score. The variation in themes Godzilla receives in Godzilla vs. Biollante is in my opinion a strength of the score.

Akira Ifukube's Godzilla theme from the Heisei Series, specifically the Godzilla vs. King Ghidorah variant. Godzilla vs. King Ghidorah marked the first film where Ifukube combined the amazing intro to the Mothra vs. Godzilla theme with the Godzilla main title. This proved to be a winning combination, producing the most iconic version of Godzilla's theme. None of the other subsequent films really matched the triumphant version of this theme in Godzilla vs. King Ghidorah, but I will give mention to its great use in Godzilla vs. Mothra when Godzilla rises from Mt. Fuji, and in Godzilla vs. Destoroyah, where it is slower, befitting Godzilla's last stand.

My last choice might come as a surprise to some people: Takayuki Hattori's Godzilla Theme from Godzilla vs. SpaceGodzilla. While Hattori is often dismissed as one of the series' most forgettable composers, I enjoy his score for Godzilla vs. SpaceGodzilla (not quite as much for Godzilla 2000). Hattori's unique Godzilla theme perfectly suits the determined anti-hero Godzilla as he sets out to defeat SpaceGodzilla and save his son. This theme has at least two variations, a slower-tempo version and the faster upbeat version that plays as Godzilla passes through Kagoshima and Kumamoto towards Fukuoka. I love this use of the theme, and it stands out as my favorite piece from the film and one of my all-time favorite Godzilla themes.

Honorable mentions go out to Godzilla's theme from the 1954 film ("Godzilla's Rampage"), Kow Otani's Godzilla theme, Godzilla's theme from Terror of Mechagodzilla, and Hattori's Godzilla theme from Godzilla 2000: Millennium.

Godzilla's theme in Shin Godzilla (Persecution of the Masses) is my favorite, but it's closely followed by the original, Godzilla 2014's theme and Godzilla's theme in GMK.

5. 1999 theme

4. 1954 theme

3. 2001 theme

2. 1991 theme

1. 1975 theme

Something of an "honorable mention" I suppose, but I always felt that Sato's best Godzilla theme (he always wrote a new one) was from Godzilla vs. MechaGodzilla. I wish he was given the chance to develop it further--After three attempts at Godzilla he really nailed it here.

It's extremely overlooked and most fans don't even recall it. I think it serves as an excellent foil to the big-band style score, fitting Godzilla very well. Take a whirl:

Godzilla's Theme from Godzilla vs. MechaGodzilla