Good character development is at the heart of any good piece of entertainment. Weather it's a television show, movie or novel if the characters don't develop then what is the point? How the characters react and change due to the things that happen to them is the primary and most interesting source of drama.
Game of Thrones is one of the most popular shows on television and the way the characters change and develop is a big part of the reason why. Take the character of Jamie Lannister. When we first meet him he's brash arrogant, and in a incestual relationship with his twin sister. Then he pushes a child out of a window. You would think him unredeemable and that he'd always be one of those characters that you'll forever love to hate. Then in season 3 after he falls victim to a act of brutality and you start to see his redeeming qualities. His love and loyalty to his family. His bravery and willingness to sacrifice himself for others. It's no coincidence that you start to see more of these qualities after he loses his sword hand. A cataclysmic event for someone who views themselves as a warrior. That hand represented everything he was, a spectacular warrior, arguably the best in the kingdom, Afterwards we watch as he set's out to discover who he is without his sword hand and become a better person. Just as thrilling to watch is Sansa Stark's transformation. A deconstruction of a fairy tale princess Sansa goes from being doted on by her parents to being held captive by her family's enemies and psychologically tortured by her husband to be, the psychotic boy king Joffrey Baratheon and his diabolical mother Queen regent Cersi Lannister. She starts out as a naive child who thinks life is a fairy tale before she starts learning how to manipulate from those around her. Her situation is improved somewhat when she is "rescued" by resident magnificent bastard Littlefinger where she continues her education in manipulation and treachery. Over the course of six seasons she goes from a guileless little girl to one of the strongest players in the game of thrones.
Breaking Bad's Walter White is a classic example of good character development. The show's creator Vince Gilligan said he wanted to take Mr Chibbs and turn him into scarface and boy does he deliver. When we start the series Walter White is a meek and pathetic figure. Everything about him, even his car screams pitiful and unremarkable. We watch his journey from an inept meth manufacturer to the ruthless criminal mastermind Heisenberg. In the beginning Walter is diagnosed with lung cancer and he starts cooking meth to make enough money to ensure they are financially sound after his death. As the series progresses and he makes more than enough to take care of his family, then more than they could probably even spend it becomes apparent to us if not to him that it's not about the money anymore. Walt has taken a walk on the dark side and he likes it! Eventually becoming drunk off of it until he's bullying his surrogate son Jesse into staying in the meth business, ordering hit's godfather style.
Another Tv show that does a great job developing it's characters is Sons of Anarchy. Similar to Breaking Bad we watch Jax's journey from anti-hero to villain and subsequent redemption. In no ways a saint the Jax we see in season one is different from others in the club. He's considered an idealist. He frequently goes against his step father and the clubs leader, the ax crazy Clay Morrow, coming up with less violent solutions to the problems the club faces. He tries on multiple occasions to leave the club and the violent biker lifestyle behind. By the final season we see the broken man he's become. Racking up a body count that would do Jason Voorhees proud he has become what he once despised and raged against. Not even the brotherhood he once considered sacred is off limits as he willingly condemns a member to death just so he can better manipulate a rival gang leader, something he never would have done in season one.