Some comic book readers follow characters while some readers are loyal to specific publishers, some readers follow a specific artist and buy whatever he or she draws, regardless of the character or publisher they're working on, other people do the same sort of thing but with specific writers.
I used to slavishly follow artists. Having grown up with two artistically-inclined young parents, surrounded by art and design books, I only paid attention to the artists (despite loving to read and write.) I did this to such a single-minded extent that I couldn't even have told you who was writing the comic books I bought. By the time I was in my early teens, I knew that I liked Frank Miller, but that was mostly because he could draw too! By the time Watchmen came out, I'd already dabbled with books like Swamp Thing and V for Vendetta, so I came to recognize that Alan Moore was doing some interesting things. Meanwhile, if John Byrne drew something (anything), I'd jump on it even if I hated the story. And even knowing that I liked Alan Moore and Frank Miller, if I didn't like the artist they worked with, I wouldn't buy the comic book, no matter how interesting in seemed. By the same token, even if I had little interest in the way a book was written, if an artist I loved had drawn it, I tried to buy it. Hence owning a lot of rather disconnected John Byrne and Alan Davis books, and a slew of odd, single issues drawn by people like Philip Bond and Bill Sienkiewicz.
Over time, it would be nice to say that I made a conscious choice to open my mind, to broaden my comic book horizons and actively pay attention to the writing. But as with many evolutions, it happened when I wasn't looking, and completely unintentionally I woke up to the fact that I was beginning to value writing as highly as art. I'd always liked the writer / artists who created their own comic books entirely. I love Moebius, Los Bros Hernandez, Ted McKeever, Paul Pope, Adrian Tomine, Robert Crumb, Chris Ware, Osamu Tezuka, Dan Clowes, and Mike Allred, but I told myself that I was just crazy about their art (and who wouldn't be?) What I didn't realize was how much the quality of their writing was affecting my tastes. These independent comic book creators were gradually changing my perception of what constituted a good comic book.
Back in the realm of non-solo created comic books, I was beginning to (completely unconsciously) favor certain writers. About 5 years ago, just as I was becoming aware of the internet presence of comic book community, a friend was telling me about Grant Morrison and I asked what he'd done, only to realize that not only did I already knew his work, but I owned a lot of what he'd written. This was quite a shock to me, and as I began to look at my shelves with a different eye, I realized that my shelves were heavily weighted with writers. Here was a ton of Warren Ellis, Neil Gaiman, and Brian K. Vaughn. On some of those books, I didn't even care much for the art! Somehow, without ever intending to, story had gradually become as important to me as art.
I love the idea that these writers' comic books somehow crept onto my shelves of their own volition, but I know that on some subconscious level I must have been seeking them out. The great part about finally noticing and acknowledging my preferences is that it enabled me to do two things; First I could now actively seek books they had written, which added a lot less of the randomness to my comic book enjoyment, and second I could now look for books by good writers without needing the art to carry the story so heavily.
The next step was encountering people who followed certain characters or publishers. Again, this was something that I had thought I didn't do, but on further evaluation, I found it to be false, even if this wasn't always reflected in my reading choices. To explain, apart from Hellblazer, which is a sort of anomaly in that I always read it and it (almost) always satisfies, I had become too attached to certain characters. I say "too attached" because it actually prohibits me from slavishly following them because I can't stand to read them if they acted in what I perceived as "out of character" or failed to look as I imagine them. Again, this only became clear to me when a friend pointed out a poster that I used to have framed in my living room, of Elektra and Daredevil, beautifully painted by Kent Williams. We discussed how it wasn't how she "really" looked, as if she were a living person. I explained that I couldn't read anyone but Miller's writing of her, and it was then that we admitted that in our minds she exists and she looks and behaves the way she is depicted in Bill Sienckiewicz and Frank Miller's Elektra: Assassin. While I tried to read other comic books about the character, they have never worked, because they are the only artist and writer who I feel "get" her. A lot of this has as much to do with the fact that this was my most intense, immersive experience of reading about the character.
The same goes for characters like Batman, the X-Men, or Superman. Even though I don't follow those characters from book to book, as some people do, I feel deeply sentimental and connected to them. Because some specific book imprinted itself deeply on my psyche at some point bringing them to life for me, I am now uncomfortable stepping outside of that specific picture I have of them. Therefore "my" uncanny X-Men will always be Byrne and Claremont's, and any X-Men comic which doesn't work with this, doesn't really work for me. Same goes for Waid and Ross' depiction of Superman in Kingdom Come; It might have started life as some kind of Elseworld story, but for me that is a very believable depiction of the older Superman I used to enjoy as a young man in Byrne's Action Comics. It was so close to my own assumptions about the character that it worked for me. Batman is a much trickier sort of a character, initially brought to my attention in Barr and Davis' Detective Comics run, but developed in all sorts of ways by people like Morrison and McKean in Arkham Asylum.
The list goes on, but you get the idea - my connection to characters doesn't make me follow them like some readers. Instead my personal affection for certain characters has almost created an aversion to following them because reading them in what I perceive to be "out of character" is so annoying. Therefore I'd have to say that not only do I not follow characters in comic books, but I tend to avoid them for fear of disappointment.
Finally, this year I've begun to understand how people can become loyal to a certain publisher. That isn't to say that I've become more or less interested in DC over Marvel (or vice verse.) Sad to say (and I hope this doesn't offend), but they really don't seem that different to me. Many people have tried to convince me otherwise, and I see what they're saying, but the differences seem superficial to me. No, the area where publishers are really standing out is in their independence. Creator-owned comic books are increasingly where the quality lies and so-called independent publishers allow for this. Creators are more adventurous, the stories drive the marketing of the books (rather than marketing driving the story, as can happen so often with the big two), and because there is a sense of personal ownership and responsibility, creators are more likely to invest themselves into the book for fear of damaging their reputations.
Going back to when I was a lone kid reading what I could find, only following artists, it was the writer / artists who I mentioned above that showed me there was more to comic books than visuals, and they all got their start in offbeat, independently published comic books. Allowing for a specific kind of flow between art and words, I'll always seek them out, but the lesson I've taken away is that the obvious quality are increasingly going to want to publish with companies who allow them to own their creations.