A great deal of virtual ink, which is nothing like actual ink save when used in a metaphor, has been spilled on the popularity of The Melancholy of Haruhi Suzumiya. It is fast becoming a sort of shibboleth, to identify those who have crossed the threshold to become a hardcore anime fan, by which I mean the sort to attend conventions and spend actual money on merchandise, official or otherwise. Like Neon Genesis Evangelion, whatever your feelings on the show itself, at least you have heard of it, especially if you actually do attend a convention. Also like NGE, it is probably not a very good first anime to introduce to the non-fan.
One of the many criticisms I have seen levelled at MoHS is that Haruhi is Not A Nice Person. From the viewpoint of a person watching the show for the first time, she's selfish, she's rude, she's arrogant, and her actions either border on or cross said border into anti-social personality disorder, depending on how charitable one is feeling. Yes, she gets better over time, but that does not change the truth-value of that descriptor at the beginning of the series, and from certain actions throughout.
The question is then posed: "how can you like a character like that?"
The answer I always give is "I don't." Which often requires me to clarify the differences between "don't like", "dislike", and "hate" (a matter of degree, with "don't like" meaning a mere lack of attraction). And then I am asked why I love the show when I don't like the main character, which kind of leads to a rather longer answer.
As a general rule, I've always been somewhat more interested in what could be considered the side characters to a show than the main character. Now, this also includes the co-protagonist type of character, or a character who may be just as important as the main character, except that her name isn't the one in the title. This started way back with Ranma 1/2, when I ignored Ranma for the far more identifiable (at least for my adolescent self) Ryouga, who helped me realize that the whole teenage angst thing was very silly, although I do remember hoping that if I ever got depressed enough I could possibly fire huge fireballs from my hands, which is always cool. After that I latched onto Shinobu in Love Hina (as did a huge number of other fanboys, if reports are to be believed), with brief sojourns into Motoko-land when she got her featured chapters, above Naru and Keitarou. Sylphiel (or Xelloss, when NEXT rolled around) for Slayers, Skuld in Ah My Goddess, Sasami in Tenchi Muyo, and quite obviously Tomoyo for Card Captor Sakura.
For more recent anime, off the top of my head, there's Nodoka from Negima as pretty much Shinobu 2.0 (new and improved version; she's a bibliophile, which ups attractiveness severalfold), Maria from Hayate the Combat Butler, Misao from Pretty Sammy (but not quite, I hasten to add, her magical girl form Pixy Misa), Koyomi from Azumanga Daioh, Tessa from Full Metal Panic, Ryou from Clannad (isn't it sad ;_;), Lily from Gargoyle of the Yoshinagas, Akane from Magic User's Club, Kazumi from Shakugan no Shana, Henrietta from Zero no Tsukaima, Mio from Zettai Karen Children, Miyuki from Lucky Star… you get the picture. Mahou Shoujo Lyrical Nanoha, as usual, is a special case: in the first season, I latched on to Fate, as the rival to main character Nanoha. In the second, I bypassed pretty much everyone else to become enamoured of Shamal. And in the third season, I remember wishing that Caro got more screentime.
And if you're wondering, for the case of MoHS, I'm torn between Mikuru, Yuki, and Itsuki. Yuki's appeal is fairly obvious to (male) fans of the show, and Mikuru is extremely effective in her purpose of being moe. Itsuki I'm intrigued by in the same way I was intrigued by Xelloss: he's highly intelligent, somewhat playful, and willing to infodump. This may be why I place so much attention on his distaff fanfic counterpart in the genderbending variation.
I don't think there's any link between these characters other than Not Being The Main Character(s). (Well, apart from Ryouga, Xelloss, and Itsuki, they're also all female, so.) There's just something about these characters which strike my fancy; alternately, there's something about the position of main characters which leads me away from them. Maybe it's a sense of rooting for the underdog, for the character who'll never get as much fame as the one in the spotlight. This seems borne out by my changing tastes with regard to, say, Tenchi Muyo/Pretty Sammy: I liked side character Sasami in Tenchi Muyo because she was pretty level-headed (compared to everyone else in the cast) and cheerfully helpful to everyone else. In Pretty Sammy, however, while Sasami had the same traits, Misao blindsided me with what TVTropes calls woobification: she's painfully shy, she has a lonely home life, and she gets turned into a magical girl (possibly her inner, unrestrained self) without her knowledge in order to fight her best friend. The trick here is that it's not played up for too long, and Misao gets plenty of support from Sasami, as well as her inner strength; her revelation and acceptance that she is Pixy Misa in Magical Project S still makes me cheer a little every time I watch it. Also, it's not like Pretty Sammy is all that serious, so it doesn't get crushed under the weight of its own angst.
Anyway, moving on from that digression, I can't really think of any reason why I prefer side characters more than main characters other than what amounts to coincidence. There's a certain set of character traits and habits which appeal to me, with some aspects overriding others depending on how they're handled, and I'd be just as happy if they're on a main character (say, Yomiko from Read or Die) as a side character. I suspect that for many cases, the character traits I like are simply better suited for side characters than main characters, at least in terms of market research or established tropes. If characters were reduced to colours, and using extremely simplified and cliche plots, Red would be the leader, bold and bright, while I'd actually gravitate to Blue (or Green), the intelligent, quiet (as in doesn't raise her voice, rather than doesn't talk at all), inventive, and probably bespectacled character.
(On a tangent, dominant colours are indeed important when it comes to costume motifs in a group. Red tends to be given to the leader, maybe yellow as second-in-command, with blue and green somewhere in the background, and the others apart from white and black in the middle. It's pretty common, and thus also commonly subverted.)
Or there could be something which makes my eye just slide over the main character. I don't know what or why. Maybe it's a psychological disorder or something.
All this is why, when I am reminded again of Haruhi's more negative actions, I remind myself that Haruhi is actually a character in the show. Not because I forgot entirely about her presence (after all, she's the driving force behind the story, and her name is in the title), but that she's a main character. To me, Haruhi herself is about as personally interesting as a recurring plot device, or perhaps a symbol of the show, with as much significance as the SOS Brigade logo or the big bold "H". If I want to represent the show, I use a picture with her in it. If I want to represent why I like the show, I'd focus more on Mikuru or Yuki.
Some fans of Lucky Star focus on Konata and Kagami, and when I mention that my favourite character is Miyuki, there's always a significant pause, which I imagine to be their brains shuffling cards around before turning up the relevant character profile, and then the response: "oh yeah, her." Miyuki is there, she's part of the group, and she's pretty significant in her own right, but she's irrelevant to what these fans enjoy the show for. This is quite similar to how I feel about Haruhi: she's there, she's not the reason I like The Melancholy of Haruhi Suzumiya, and my reaction upon being reminded that she's not really a nice person is "oh yeah, her."
Incidentally, Kyon is an interesting case: I don't really think about him as a character, because the show (and the books) do so well a job of making him an audience surrogate that I have trouble thinking of him in any other way. He's kind of out of the competition for Favourite Character, since he's supposed to be me, and I can't really be a Favourite Character to myself.