When it comes to the common theme of Zanpakuto in Bleach, they generally share the same trends, except in certain circumstances.
As Byakuya narrated to us, a Zanpakuto is normally expect to generate a large weapon or effect when the Shinigami goes from Shikai to Bankai. The few exceptions to this rule among normal Shinigami are Unohana, Yamamoto, and Ichibei. These three can be called 'exceptions' because they are among the three most powerful Shinigami in the series, and their Bankai do not "expand" the form of their Shikai. Instead, their Bankai can be said to "compress" the power of their Zanpakuto to make their power even more potent. Ichimonji is even more unusual because, given its power over "Names", Shirafude doesn't expand its ability to utilize "Black" - it instead gives Ichibei the power to "Re-Name" whatever he has blotted out with Ichimonji, which is arguably even more dangerous than simply using more "Black".
But as of late, I have noticed that there are three Zanpakuto that have completely unique effects, and are functionally different from every other Zanpakuto in the series. One of these was commonly known, the other was hinted at two years back when its Bankai was revealed, the most recent one only showed up in the past month, but it is only with the recent chapter that it has been fully confirmed for the first:
Zangetsu, Sode no Shirayuki, and Nozarashi.
We have known about Zangetsu's unique Bankai for over a decade. Even though it was a "fake" Zanpakuto created by Ichigo's Quincy power, Tensa Zangetsu compressed Ichigo's power, rather than expanding it, as most Bankai do. But what makes Tensa Zangetsu different from Zanka no Tachi (from a blazing inferno to a charred blade with all the heat compressed along the edge), and Minazuki (giant manta creature to a blood red blade of acid), is that Tensa Zangetsu transforms Ichigo's Shihakusho and augments his combat speed and physical strength by a considerable degree.
Now Ichigo has his "true" Zangetsu. While he has yet to show his Bankai yet (and it is implied that he is not even in Shikai), we saw that Ichigo can use Zangetsu to make himself undergo a Hollow-like transformation. In the past, Ichigo underwent Hollowfication using a Hollow Mask, but now he has used the true Zangetsu to physically transform his body into a likeness akin to the fused Tensa Zangetsu from "Deicide". This is an ability unlike anything we have ever seen before in the entire series, especially from a Shinigami Zanpakuto. It truly shows that Ichigo is more than just a Shinigami - he is also a Hollow, and a Quincy as well.
But what struck me the most about Ichigo's transformation is how much his appearance resonates with Zaraki's appearance when Yachiru (should probably say Nozarashi from now on) triggered his Bankai. Aside from breaking the record of the fastest attained Bankai in existence, Nozarashi was a long anticipated Zanpakuto. Not only was it long anticipated, but its power definitely lives up to the one who wields it. But more than that, it also disproved the notion of a constant-release Zanpakuto (propagated by Ichigo's "fake" Zangetsu) because Zaraki does have a release command, and that command transforms Nozarashi from a chipped katana into a massive war-cleaver/axe as almost as big as Zaraki himself.
The Bankai is where things get interesting. When Yachiru gives Zaraki the power of Bankai, Nozarashi actually shrinks. It roughly retains its form, but the blade is much smaller, and the tassel and attachment at the top of the blade disappears, leaving it bare. It is much like Tensa Zangetsu in this regard, but the biggest change is Zaraki's overall appearance, because his skin turns completely red, he grows horns and appears to have a black marking in the center of his forehead. But more than that, the increase in Zaraki's physical strength and speed in his Bankai is astronomical, completely overwhelming Gerard, who had previously bested Zaraki when Zaraki had Nozarashi released and had taken off his eye-patch. That said, because of how new it is, his body couldn't handle the overwhelming power it put out, akin to Ichigo over-stressing the bones of his body from over-using the hyper-speed combat of Tensa Zangetsu.
This is also akin to how Rukia has to be careful with de-thawing from when she reaches Absolute Zero, lest she damage her own body as well.
NOTE: I'm saving this for last because I want to clarify that I don't intend to start any arguments over how the power works. For the purpose of this theory, I won't choose to debate the issue.
Depending on how deeply you look into Sode no Shirayuki's ability over the course of the manga, you can see that Kubo has been setting up the reveal about the nature of her Zanpakuto ever since the Aaroniero fight. While it is a Zanpakuto that can use various techniques to freeze Rukia's opponents, the core ability of Sode no Shirayuki instead affects Rukia herself. This is similar to Zaraki's Bankai; this is similar to the transformation Ichigo has undergone in the recent chapter. But in Rukia's case, the effect isn't visible (at least in the Shikai), but it does affect her body.
Sode no Shirayuki gives Rukia the ability to manipulate the reishi comprising her entire body, and allows her to continue functioning even when Sode no Shirayuki reduces her body temperature to below zero Celsius, a temperature at which all of her physical bodily functions would cease to function. Not only does her body temperature reduce itself to below zero, but she can manipulate her body temperature to reach all the way down to Absolute Zero. But, akin to Ichigo over-exerting himself in regards to speed with Tensa Zangetsu, and Zaraki's arm ripping off from Nozarashi giving him too much power, Rukia can only stay at Absolute Zero for four seconds, and has to de-thaw slowly in order to not risk injuring herself.
Hakka no Togame takes this ability one step further. The sole changes to her Zanpakuto are the ribbon on the handle disappearing, and the blade turning to pure ice. What is most striking, however, is her physical appearance. Like Ichigo's Shihakusho, Rukia's Shihakusho changes into a pure white kimono/robe , and even the leggings of her Shihakusho also turn white (or that could be ice). Moreover, Rukia's hair also turns pure white when she is using Hakka no Togame, and wears a crown of ice. I've heard some people claim that Rukia can't move in this state or else she'll shatter herself; that her physical appearance is purely aesthetic. But we did see Rukia moving immediately after releasing Hakka no Togame (she wound up behind As Nodt when she released in front of him), and the fact that her Shihakusho changes form, just as Ichigo's Tensa Zangetsu did, implies that Hakka no Togame may lend towards a similar fighting style, with the Zanpakuto able to reduce her body temperature all the way down to Absolute Zero being Rukia's version of Zaraki's Oni appearance, and Ichigo's current Hollow appearance.
All three of these Zanpakuto and Bankai are completely unique from every other Zanpakuto seen thus far.
NOTE: One could count Daiguren reaching maturity and Toshiro aging along with it as a similar kind of Zanpakuto, but I'm banking on Toshiro reaching adulthood being a permanent effect of the Bankai reaching maturity, rather than a special transformation of the Bankai itself.
The question that remains is why these three are the ones who have such unique Zanpakuto, and is there anything they have in common with one another that connects them all together.
When you look at Zaraki and Ichigo, both of them possess monstrous potential compared to every other character in the series. In that same vein, both of them had something holding all that potential back (Quincy Zangetsu for Ichigo; subconscious shackles on his own power for Zaraki). The two of them were also marked as "Special War Potentials" by Yhwach, so Yhwach was aware of both of their hidden potential long before they themselves were aware.
In Ichigo's case, we know why he has such immense potential - his soul is made up of Shinigami and Quincy, and Human and Hollow, a combination which, as finally shown, affords him unique abilities and a Transcendent potential. But in the case of Zaraki, we do not know where he came from. All we know is that he was a child from the Zaraki district, in the most brutal and unlawful part of the Rukongai, who came upon an Asauchi dropped by a dead Shinigami.
In the case of Rukia, the ability of Sode no Shirayuki does speak of the potential she also possesses as a character. From my own observations, I came to realize a while back that you can judge a Shinigami's potential based on the power and ability of their Zanpakuto. It is no coincidence that all of the most powerful Shinigami in the series tend to possess the most powerful kinds of Zanpakuto, and the most powerful Bankai, and not many abilities are more dangerous or more powerful than Absolute Zero.
But what is unique about her power may point towards exactly why she has such a Zanpakuto to begin with, and why everyone else does as well: the fact that she manipulates the reishi of her own body sounds more akin to a Quincy ability than an ability a normal Shinigami would possess. The basis of the original Tensa Zangetsuwas Ichigo's Quincy power. I am not certain what this means for Zaraki, given he is the only one out of the three whose Shihakusho does not change appearance, but he does get the most drastic physical transformation.
NOTE: Oh, and Zaraki's the only one without a mono-color Zanpakuto, though Ichigo may be going the Yin-Yang route.
But it is not just Quincy power that may play a factor into the entire issue. If Ichigo is any indication, all four soul types may play a role, because the culmination of all four soul types has been implied to be what produces the power of a God.
I stated this in my last review of a Bleach chapter:
While some people would be annoyed by this, I see this as fitting with the overall theme of the original three Schutzstaffel so far. While Lille was the only normal Quincy among the trio, all three of them possess the power of a God - Pernida and Gerard are aspects of the Soul King, while Yhwach's Schrift made Lille into one in his Vollstandig. A common theme among these possessors of the power of God is their insane survivability; Pernida's "Progression" allows him to regenerate from being blown apart (only cancerous cells seemingly killed him for good); Lille Barro possesses intangibility, and was able to regenerate into a more powerful form after his head was blown off; "The Miracle" has allowed Gerard to recover from virtually everything the Shinigami have thrown at him, and he keeps on becoming more powerful with each recovery.
If there is something that the three of them collectively remind me of as well, it would be Aizen in "Deicide". He fused with the Hogyoku back then, and we saw that inflicting injury upon him after the Chrysalis stage led to Aizen evolving further and further in power in response to the injuries. When Gin "killed" him, he evolved into his Seraph form, attaining a form and power "transcending both Shinigami and Hollow"; when Ichigo struck him, his subsequent anger caused yet another transformation and increase in power.
In a sense, Aizen was all three of the Schutzstaffel rolled up into one: regeneration from any injury, no matter how severe (Pernida), the power of teleportation (Lille displayed this in Vollstandig), and he progressively became stronger with each injury he recovered from (Gerard). This is not counting the Hogyoku's ability to "manifest the heart's desire", a very similar trait also shared by Gerard's "The Miracle": everything "The Miracle" has allowed Gerard to do was in response to the emotions of his adversaries.
Ichigo also qualifies for this trend, because the moment he attained the power of a Transcendent Being, according to Aizen, was during his fight with Ulquiorra - the fight where he had a hole blown through his chest, and his Hollow power saved his life and transformed him into H2 Ichigo.
This is only a possibility, mind you, but this idea of a "God reiryoku" may wind up tying everything together. If Zaraki's appearance now is like that of one of his Zanpakuto spirits (I'm assuming a second one gave Zaraki the name of his Zanpakuto), then it may confirm an idea I just had in regards to these three characters: When these three characters utilize their Zanpakuto, particularly in Bankai, their physical appearance takes on a form akin to their Inner Spirits.
The same holds true for Lille, Gerard, and possibly even Aizen. But, instead of simply taking on physical traits similar to their Inner Spirits, the three of them essentially transformed completely into said Inner Spirits. The Light Colossus is this for Gerard; the second Vollstandig form was this for Lille Barro; Aizen's final appearance is what his Inner Spirit would like as a Hollow, with his third form potentially being its appearance in Aizen's Shinigami Inner World.
I cannot be entirely sure about Rukia and Zaraki, given we do not know what bloodlines those two came from, but this is definitely the case for Ichigo, as is being proven with his most recent transformation.
So there you have my theory on the nature of Ichigo, Rukia, and Zaraki's Bankai: their unique Bankai may be the result of all three of them having a Quincy-Shinigami heritage, and/or having been born into bloodlines or circumstances where all four soul types exist within their souls, and give them the potential to attain the power of a God.