There are several elements in play that make Breaking Bad an exceptional dramatic series. But on the whole, I think what makes it work for me is that there is nothing gratuitous about it. There is a kind of lack of extremes and a fairly light amount of artsy filmmaking that plays just right.
I find myself attracted to the Breaking Bad series despite myself. Having once been a follower of a number of HBO & Showtime series, the latest being the first season of Dexter, and some fraction of the first season of Burn Notice I have sworn off the genre. It was as I was watching Andre Braugher's entree into the arena that I began to recognize nastier aspects of the formula. Take a bad guy, make him smarter than everyone around him, and humanize his dirty business as he attempts to make his life work by focusing on the personal battles he must face. I surmised at length that this was a particularly seductive and unctious blueprint which gradually wore down a viewer's moral sensibilities by alternately shocking and soothing. Some genius writers figured out how to make good people cheer for the bad guy, and see him as the product of the system, a kind of necessary evil. A good evil. Evil with a human face.
Before The Sopranos, nobody had figured out how to captivate American audiences in quite this way. The bad guy was always pretty straightforwardly bad, and you basically liked him for his badness. Lt Butnz from Hill Street Blues and Detective Sipowitz from NYPD Blue came close. They were essentially good guys with bad ethics, but they were working against the worst of the worst - so there was an easy way to justify this. On the other hand shows like NCIS, JAG, but most importantly Law & Order (especially SVU) and CSI, the the wildman formula was reversed. A clean, bright, superstar collaborative team could indeed handle even the most heinous crimes while maintaining sterling ethics.
But on the fundamental side of soul-poisoning was Oz, The Sopranos, followed by Deadwood, Baugher's short-lived Thief and most recently Boardwalk Empire. Fundamentally bad guys doing fundamentally bad things with rationalized ethics. I adopted an attitude about protecting my soul and at some point decided to stay away. (And watched 24, CSI Miami & House instead)
The Wire stands as a exception in all of this, as does The Sheild. Both of these shows had such great actors and so many interwoven subplots with large casts, that even though they were ostensibly about one person, there was so much more going on that some of the fundamental poison could be overlooked. With The Wire however, my patience waned after a short period just before, I am told, the series got really good and became something of a social commentary on what 'black' life is really like. I didn't really have patience with that attitude with The Corner, despite my admiration for Charles Dutton. But there can be no denying of the actng talent of Idris Elba. What set The Wire apart critically was that it was one of the rare shows that broke through the 'Ron Glass Ceiling' by having a critical mass of intelligent middle-class black charaters that must inevitably conflict over nuanced matters. American audiences can count those shows on one hand. Yet that was not enough of a draw to keep me interested in Stringer's schemes or McNulty's quest. Instead I found myself much more drawn to Michael Chiklis' drama of trying to outwit, on a day by day basis, an entire police department doing good work, and panicked deception in order to maintain a coverup of an extraordinarily dirty deed done long ago. Here was an angle on the formula that hooked me. A good guy who has done horribly wrong and tries desparately to hold it all together in order to survive and do future good. This involved family, like the Sopranos, and a persistent antagonist that changed each season, unlike any other dramatic series (except perhaps Harry Potter's defense against the dark arts instructors). So the Sheild, despite its soul-staining brutalities, passed my defenses.
I should also say of Boardwalk Empire, Rome and what I surmise about Game of Thrones is that they all were in their own way costume dramas derivative of HBO's original groundbreaker Oz. You put everybody into a period Hell and watch how they sizzle. All soap operatic melodramas with extreme sex, violence and duplicity. Bam.
Breaking Bad, by its excellence and uniqueness, demonstrates something new that illustrates all of these other dramas and in many ways surpasses them. But I think I'm going to finish out the fourth season before I say anything further.