Ned Stark doesn't recognize that Queen Cersei or the relatively low-born Littlefinger can actually be threats. So he, from misguided mercy and possibly benevolent sexism, informs Cersei that he knows her secret and intends to act against her, never imagining that she will dare to harm him or the king, in order to keep her incest, adultery and cuckoldry secret. Ned makes his disgust with Littlefinger clear and contemptuously refuses to take or even pretend to consider Littlefinger's advice. Ned states that he will act in a manner which is clearly opposed to Littlefinger's best interests. He is nonetheless quite shocked that both Littlefinger and Cersei act in ways which, while dishonorable and underhanded, advance their own interests to Ned's fatal cost. Ned's pride in his status as Hand of the King, Warden of the North, and Lord of the oldest House makes him blind to the fact that he has a very weak position in King's Landing, especially after Robert's death. Ned has a very rigid stance on honor and rectitude, one that he's unwilling to part with even at the cost of his own life. By the time he is willing to shelve his honor and perhaps even regret his extension of mercy to Cersei it's too late to save his life or spare his daughters from some very hard times indeed. Ned thought people should have obeyed him because it was the right thing to do. That may have been true but in Ned's world and ours getting people to do the right thing may require an application of force, a realistic threat of the same and an appreciation of other people's self-interest. Ned lacked all of that.
Vito Corleone doesn't suffer from either mercy or honor (as least as Ned Stark would understand the term) but he does have Ned's pride. And it's this pride which makes Vito think he can impose his personal distaste for drugs onto the entire NY Mafia. It's pride which makes Vito overestimate Luca's abilities and his own craftiness, thus throwing away his most valuable asset even before the war begins. It's pride which makes him think that his primary businesses of loan sharking, gambling and extortion are more "respectable" than narcotics trafficking. It's pride (an unwillingness to look into details?) which leaves him unaware that Paulie is a traitor until it's too late. Similar to Ned's contempt for the pimp Littlefinger, Vito has contempt for the pimp Solozzo. In Vito's worldview, real men are not pimps so he dramatically underestimates Solozzo and his supposed patron Tattaglia. Like Ned with Cersei, Vito simply can't take Solozzo as seriously as he ought to, in part because Solozzo violates Vito's ideals of gender and masculinity. Vito was under the impression that a pimp meekly accepts dictates. He certainly doesn't murder your top enforcer, bribe your driver/bodyguard, kidnap your counselor and adopted son and almost succeed in knocking you off on two separate occasions. Vito doesn't pay the same price that Ned does but the initial impact is the same. Like Ned, Vito's oldest son has to take over family leadership a few years before he's ready.
Sonny possesses all of Vito's martial strengths and then some. Like Robb Stark, he's won numerous battles with his family's enemies. Although calling Sonny honorable might be a stretch he does very strongly believe in protecting the younger and weaker members of his family, a positive quality that much like Robb's honor is calculatedly turned against him and used to bring about his demise. Just like Robb, he is betrayed by someone very close to him as much for personally vindictive reasons as for business. Sonny's death forces Vito to sue for peace. The Corleones lose respect and power as the rival Barzini Family seizes the top spot in the NY Mafia. Robb marries for love and is murdered by his spurned putative father-in-law. Sonny tries to protect his baby sister and is set up to be murdered by his brother-in-law. Both Robb and Sonny take actions based on love. These things are totally understandable and even admirable but are strategically unwise and strictly speaking violations of expected protocol. The Corleones are "luckier" than the Starks in that Sonny's mistakes result in only Sonny's death. Both Sonny and Robb die in a case of literal overkill from which there was no possible escape. Both Sonny's and Robb's corpses are mocked and mutilated after their death as a sign that their power (and that of their family?) is at an end.
In The Godfather the Corleones had Michael to step in after what looked like total disaster, get a satisfying revenge and make the Family even stronger than before. Michael was able to learn from his father's and brother's mistakes (and his own loss-the death of Apollonia) and get a crash course in being a boss from his father.
In the series A Song of Ice and Fire, it's an open question as to whether Martin even wants to venture down the Stark revenge path. He quite evidently enjoys subverting expectations, maybe too much so at times for my taste. As Lord Commander Mormont once told Jon Snow, the war in the South is completely meaningless compared to what's beyond the Wall. Martin may well feel the same way. He might have pulled the greatest bait and switch of all time, that is if you happen to be a Stark fan and/or were expecting some Stark payback. The Red Wedding could be Martin's way of beating into everyone's thick skulls for once and for all that the Starks are not central to his story-at least not in the way that we might have originally thought. His story is deeper and more grandiose than that.
Obviously if you've read all the books, please don't discuss things which haven't happened in the HBO series yet. That said, you really should read the books....