Dany is busy eating a horse heart, because if she doesn't, her fetus will be born weak, deformed, or (GASP) female. She manages to finish the entire heart and keeps it down, much to the satisfaction of the Dothraki crones. They proclaim that her kid will be the "the stallion that mounts the world." Dany will be so proud, since not everyone's son gets to be a gigantic horse that humps planet earth. She names him Rhaego, a cross between her brother Rhaegar and her husband Drogo. Rhaego is the Dothraki version of Darth Vader, destined to fulfill some crazy prophecy.
While this is going on, Viserys is frequenting the local markets, getting wasted on wine. He finally shows up at the ceremony, but he's drunk and carrying a sword. It's forbidden to have steel in Vaes Dothrak, so obviously Viserys built a time machine and returned with a plastic sword, because nobody would be so stupid as to directly defy the law of a vicious, war-centered race who wouldn't hesitate at all to kill an annoying beggar king. Viserys then draws the sword, waves it around, and threatens Dany's kid. Yes, the same kid who the Dothraki see as their future planet humping, prophecy fulfilling, Darth man-horse. This is obviously not a smart thing to do, but Viserys was never the smartest of men. In response, Drogo calmly kills him by pouring molten metal over his head. Finally, douche Viserys gets whats coming to him, and Dany severs the last binding tie to her old way of life.
Robert is dying, gored by a boar during his hunting trip. This is far too convenient timing, and I subscribe to the Varys-hinted theory that the Lannisters were behind it. Before Bob dies, he names Eddard protector of the realm, very similar to what that old emperor did in Gladiator. Eddard doesn't want the throne, and that's why "it must be him." King Bob's decision isn't going to sit well with the Lannisters, and Ned will probably be enslaved and forced to fight in the Colosseum for the amusement of the King's Landing mob. Then he'll reveal his identity as Eddard Stark, Warden of the North, Lord of Winterfell, Hand of the King, loyal servant to the true King, Robert Baratheon; father to a crippled son, husband to a boring wife, and he will have his vengeance, in this life or the next.
On his deathbed, Robert makes Eddard promise to take care of his children. Ned can't bring himself to tell Bob the truth about his kids, so he silently thinks of all of Robert's true children, scattered around the realm. Can you imagine Catelyn's face when Eddard brings back ten more bastards to take care of, even if they aren't his?
Eddard plans to crown King Bob's eldest brother Stannis, beacuse Joffrey isn't his true heir. Robert's younger brother Renly offers his help to grab power by capturing Cersei's kids, but that is too dishonorable for Eddard. Let me repeat that: it's too dishonorable to temporarily capture the kids of a woman who not only has kids with her brother but also attempts to kill crippled, comatose children. Littlefinger suggests a different plan, recommending that they make peace with the Lannisters, bide their time, and reveal the incest later on. Eddard can't stomach playing nice with the Lannisters, because they killed Jory and tried to kill Bran. However, Eddard isn't stupid: he knows he needs more swords than he has, so he arranges with Littlefinger to purchase the City Watch's support, just in case.