For every medium, there are few masterpieces that transcend the genre and become something special. Since I consider anime, as a genre, to be just as legitimate an art form (despite the bad rep it often gets), I will also review Bakemonogatari as a work of art, and it is irrefutably one of the special few anime series that fully capitalize on the strengths of the anime medium.
People have complained that the story is too episodic, too disjointed. However, the virtue of Bakemonogatari's storyline is that it is so minimal. In all senses, this anime is a character-based experimental, and an elaborate storyline would actually detract from that experience. There are plenty of anime out there that thrive on plot twists and progression that keep the viewer on their seats, but Bakemonogatari isn't one. The episodic storyline is a brilliant framing device for character development and nothing more, which works out perfectly for this particular anime.
As usual Studio SHAFT splurged on art. This is definitely a series to be enjoyed in high-definition, preferably with the room lights turned off. Anime, by definition, is a genre segregated from realism. The beauty of anime as a medium is that every cut is animated, so that the blemishes, imperfections, and limitations of reality can be omitted in favor of stylized, beautified perfection. Anime art style that attempts to be too realistic are bound to lose that edge and, naturally, pale in comparison to live-action works featuring comparable visuals. Anime that go all in on stylizing can often seem distracting and too detached from reality. With all of that in consideration, Bakemonogatari is one of the few shining masterpieces of the anime genre that hits the sweet spot. Everything in this anime is crisp and beautiful, from the characters to the slightest scenery detail. What would have seemed tacky when drawn are boldly stylized and symbolized, rather than allowed to compromise the atmosphere. For example, people have complained about the cuts to photographs and abstract diagrams that pop up frequently. But imagine if all of those were actually animated; it would have been clunky and distracting from the dialog. For example, Senjougahara's mother isn't a character in this anime, therefore having an designed, animated character to her credit would distract from the very small and tight cast. I don't know how much budget went into this production, but they sure splurged where it was needed (characters, scenery-porn sequences, pivotal action sequences) and were decisive in radically minimizing what would have been superfluous.
There is quite a rave about Kimi no Shiranai Monogatari and Staple Stable, and they are indeed catchy and appropriate opening/ending. Much more underrated are the mundane, ambient sound design of this anime. Just as Bakemonogatari should ideally be viewed in high-quality settings, so it should be heard with at least "nice" audio. Perhaps I had the fortune/misfortune of being an impeccable audiophile and watched the series with headphones that cost me half a fortune, but everyone should at least watch Bakemonogatari with real speakers or decent headphones. This is a series that can only be fully appreciated when the viewer is immersed in it, and laptop speakers simply won't do.
Having said all of that, the non-intrusive BGM and ambient sounds do a perfect job of accentuating the dialog/situation without, again, distracting from what is really important. Perhaps the best example is in the TV finale, where the BGM swells and fades without the viewers really noticing because they are so perfectly integrated with the ebb and flow of verbal/situational push and pull between the two leads.
The voice acting, without even the need to elaborate, are top-mark. The seiyuu for Koyomi is appropriately serious, jocular, and reflective. I especially enjoyed the sequences and inserts in which Koyomi is thinking selfish/perverted/silly thoughts. Excellent sound designing makes it sound like Koyomi's voice is really ringing inside my head, adding to the effect and how identifiable his character is. Voice acting for Senjougahara seemed a bit too fragile and breathy at first, but it was revealed to be not the fault of the seiyuu, but part of character development, but more on that will border on spoiling. Let me just add that voice acting for both leads hit the sweet spot at least by the TV finale.
All of the other elements, story, art, and sound, up to now were accompaniments to the brilliant characters of Bakemonogatari. If those elements had their virtue in garnishing the backgrounds of this anime, the characters' virtue lie in their shocking assertiveness and charisma.
Koyomi - Of all anime leads I've seen, he is one of the few truly-believable leads that are likeable. He is objectively decent-looking and decently dressed, not, as are many a blue-haired shounen characters, outrageously flamboyant. He is not an outspoken paragon of bravery and power. He is even a bit of a sociopath. However, the subtle inner stability he shows makes him stronger than Goku or Lelouch in my opinion. He isn't a social butterfly, but he would never seriously harm another person. Though he is a bit of a pervert, just like the rest of us, the viewers can't picture him ever being disloyal to his romantic partner. Koyomi's inner strength and stability are what keeps this series from becoming a typical harem anime, and such qualities of his character are what makes the viewer so strongly and ineffably identify with him.
Senjougahara - First of all, her name is awesome, just phonetically. I read that it means something like "battlefield" in Japanese, but it sounds so feminine and appropriate to her character. With that aside, if Koyomi is the steady, dependable drummer keeping beat to the Bakemonogatari band, Senjougahara is the lead vocalist that captures and enthralls the viewer. Anime is, more than anything, a visual art, so it is of course important that her every frame is perfected and beautified with adoration. Not only is she one of the most flawlessly beautiful female characters in anime, the way she poses and moves is also idealized. Imagine a girl who never does anything unsightly: never makes an unflattering face, is never without makeup (or always looks perfect without one), never goes to the bathroom, you get the idea, and that would be Senjougahara. Again, the creators of Bakemonogatari really cashed in on this aspect of anime to create a visually flawless female lead. Utter perfection, however, isn't always likeable, as none of us are perfect. Senjougahara, therefore, needs some profound flaw in order to offset her physical perfection, and that's when her character development comes into play. I won't say much more on that for fear of spoiling, but she exists not as a perfect, standalone being, but someone who absolutely depends on Koyomi to complete her. That's why their interactions work, even though they should logically have zero reason to even know each other. Senjougahara is the modern Yamato Nadeshiko, though the usage of that term to describe her may be controversial. The numerous attempts to categorize her as a tsundere/kuudere/yandere/whaeverdere have all failed because her character is grounded not on a trope, but a real-life ideal of feminine beauty. She is the culmination, or rather, an amalgamation, of decades of anime heroines that captured the viewers, male and female alike. Senjougahara and Koyomi have such subtle and inexplicable chemistry because they are both subtle, ultimately mysterious characters.
This is the one category where I admit that the 10/10 is highly subjective. Objectively, Bakemonogatari is a top-quality art form, and I firmly believe that high-profile artists, filmmakers, etc. would appreciate that Bakemonogatari is the epitome of modern anime counterculture (Suzumiya Haruhi being the mainstream crystallization of modern anime). However, you have to be looking for the right thing to enjoy this anime. If the anime you typically enjoy are Naruto, TTGL, etc. (not that they aren't fantastic either), Bakemonogatari is perhaps not for you. This series is really for people who have watched a lot of anime, perhaps even an otaku, and were drawn to the more sophisticated, post-modern aspect of the genre as a whole. It is, in a way, analogous to how Mozart is universally loved (for a good reason!), while composers like Hindemith appeal strongly to those who have developed a taste in classical music. I personally pick this series as the number one anime of all time (along with NGE) because it had all I was looking for: deep, subtle characters, platonic romance, somewhat surreal atmosphere, idealization only possible in anime, wit, and that pinch of sociopathy shown in each character, as are present in every human being. There isn't one thing about this anime that is the "hook" (though, if I had to pick one, I'd go with SENJOUGAHARA FASCINATION). Rather, every aspect of it plays its role perfectly to create a gestalt whole. Oh, and by the way, if you're like me and are desperately looking for non-moe, non-loli (getting harder and harder to find) anime made in 21st century, welcome to Bakemonogatari. This series is for mature viewers looking for a subtle, yet decisively anime experience.
Overall, if you think yourself the discriminating, intellectual beta-component of modern society (who also happens to watch anime), you will love this series. It's a love or hate type of anime, in my opinion, and if you are the type of person this show caters to, you will come to thoroughly appreciate every aspect of the show, besides just Senjougahara. If you're not, that doesn't mean you're not as cultured or some nonsense; just need to find your anime masterpiece, as I found Bakemonogatari.