
Kankuro: An average Joe, who just so happens to have a sadistic fetish for complex puppetry as weapons and wears makeup on a day to day basis
First, let's get the fangirling out of the way, shall we?
I love Kankuro with his snarky commentary, overly confident exterior, and kitty-eared Kabuki hood. And, as a quote I saw floating around the forums once said, (paraphrased) 'I didn't like Kankuro inspite of the fact that he was a stupid twat bullying small children when we first saw him, but because of the fact that he was a stupid twat bullying small children.'
That's, actually, one of the reasons that I like him, too.
A number of people have already mentioned that Kankuro's flawed nature is one of the things that they really enjoy about him and wished that Kishi would write more characters in a similar vein. I agree, but not just because he is flawed. Rather, I am most interested in how his flaws are so vastly different from those held by others in the series.
Sasuke is a dramatic avenger, whose ultimate goal of revenge is keeping him from living his life, destroying him and everyone who still cares about him.
Naruto is the hardworking, obnoxious but loveable prospective Hokage, whose faults drive him to be more ambitious, to be acknowledged.
Temari's supposed faults of being the slave-driving, independent woman are part of the basis for half of the running jokes in the show, centering around her relationship, friendship, whatever with Nara Shikamaru.
Lee...seriously, I could go on. But, all of them would be the same. Grand ideals, grand goals, grand faults and grand epiphanies.
Kankuro, on the other hand.

Picks on small children for laughs. Brashly plows forward with incomprehensible confidence, and seems to have no real goals other than the engineering of more puppets and discovering new methods of Kabuki decoration, so that his face can match whatever his newest acquisition is.
His faults are homely, familiar. He even treats his interests, a fanboyish obsession with Kabuki theatre and puppetry (i.e. seriously, he pretty much cosplays every single day), similar to how those watching the shows might deal with their everyday addictions.
And, even the one thing that might have made him stick out, the fact that he does specialize in a particular branch of fighting that involves complex engineering skills and amazing chakra control, is completely overshadowed by the introduction of not one, but two puppeteers whose skills far exceed his own (Chiyo and Sasori).
Although, he seems to have a much more companionable relationship with his puppets, particularly Karasu (who he talks to all of the time, which has to be one of the most endearing/pathetic/mildly creepy things that occurs in Naruto).
But, the point is, that Kankuro is nothing special.
Which, oddly enough, MAKES him special.
Because he's living in a world, where seemingly everyone is extraordinary.
So, for me, he becomes this wonderful touchstone. An everyman in a shounen manga, which is a rare thing, as power and its accumulation is the typical focus. Especially an everyman that is not just comic relief or just a foil (as Kankuro was throughout most of part one).

Also, whether he likes it or not, Kankuro is a part of the Sand sibs, and to me, he is the glue that holds them together. With a particular focus on the way he draws Gaara back into their family through antagonism.
Although Temari was able to stop Gaara PreTS from killing (coughcoughKankurocoughcough), it is Kankuro who keeps the relationship with his brother alive. Despite fearing and resenting the younger boy, Kankuro still interacted with him, even when it is wasn't necessary (unlike Temari).
Amusingly, it is his annoyance at being inferior in power to his younger brother and the way he chafes beneath his command that causes Kankuro's hatred towards small children. I'm thinking particularly of the line right before Gaara threatens him during the second chuunin exam (could've just been anime, I don't remember) when he tries to make Gaara stop by saying that he's the older sibling, and the redhead should listen to him. And, of course, Gaara, you know...doesn't.
Spoiler: Kankuro is whipped
Again, it just makes sense in a sweet, endearing way, without needing any of the raw power and angst of Naruto or Neji.
And I love watching the way that this connection with his younger brother grew and developed over the TS, along with the two boys. With their maturity, they've gained respect for each other. Not to mention the fact that Kankuro is finally being given a chance to be the older brother, even if its still the older brother of the Kazekage-sama. And, so his kind but prickly nature gets to shine a little bit in his affection towards Gaara, his gratitude towards Naruto, and his adamant refusal to let go.
Haha, again, I love Kankuro because he is one of the few characters, seemingly without any angst or deep underlying emotional issues. But, the only time he does get a little " OH NOEZ!" is during the Rescue Gaara Arc with that wonderful , dramatic, "...Gaara." Every five minutes.
However, for me, this just made him even more of a comfortable fit, as everyone needs to angst every once in a while. Plus, the boy has finally started to be able to emote with his siblings, and while not the astronomical Neji breaking free from his cage kind of growth, it is a gentle, soothing change.
Spoiler: Kankuro, Gaara, bonding, and love
Besides his comfortable nature and homely personality, one of the things that really intrigues me about Kankuro is his dark streak.
You know what I'm talking about, the side of Kankuro that thinks up the lethal offensive and perfect defensive machine that is Kuraori and his Black Secret Technique Machine Two Shot. Or the side that thinks it's funny, tripping Naruto up with his chakra strings. Or the part that laughs in every single enemies face (even when he's losing) just because he's that kind of a bastard.
It's harsh and wild and probably stems from his upbringing in the wilder Sand village. And is all the more intriguing when balanced against his obvious good heart: trying to warn off the Rain shinobi during the second exam, telling Naruto that he likes him, etc.
Hrm, perhaps, he is not so average after all.
Or, maybe it is just that he is given a level of depth out of keeping with his minor character status. I don't believe you could find many characters in the series who experience the same set of varied emotions, reactions, and growth that Kankuro does, especially considering that he does not necessarily need someone to punch him in the face or grab him up by the hair for change to occur.
Lastly, because this has gotten far too long and is just basically a fangirl ramble (which could literally go on for at least three more posts...hell, I could've spent just this one talking about his connection to Kabuki theatre and puppetry which I didn't even touch on really), I adore his character design.

It is totally badass and insanely interesting, with a strange meld of the Middle Eastern influence common to all of the Sand shinobi and Japanese theatrical costume. From the makeup to the props, he really is a showman, in every sense of the word. (And, I suppose he had to be. How else is a guy supposed to get noticed, when they are most ordinary, average of characters when it comes to abilities, appearance sans getup, etc.). This dichotomy also reflects that earlier division within him of light and dark, pure and twisted. And, I am utterly fascinated.
A part of me has often wondered how different of a boy he would have grown to be had he been born in Konoha. If it was the Sand village that caused the feral quality within him or it was just his inherent self.
Because that's what he is, and it's reflected in the exotic nature of his design; Kankuro is feral, untamed.
Okay, partially tamed, but you never really know if his love nips will be nibbles or great, big, painful chomps. Because, he's just that kind of average sarcastic guy, who'd find that kind of joking around to be absolutely hilarious.
No matter how much he's grown.
Spoiler: