6. Big Walder and Little Walder
Two of Lord Walder Frey's grandsons, Big Walder and Little Walder, are fostered at Winterfell as part of the agreement that Catelyn Stark reaches with Lord Walder. This is also the agreement that involves Robb Stark marrying one of Lord Walder's daughters and Arya Stark marrying one of his sons. You'll notice that in the Game of Thrones episode "Baelor," though, there's no mention of Big Walder and Little Walder — although just like in the book, a different Frey son, Olyvar, is to become a squire for Robb. Thus, it seems highly likely that Big and Little Walder won't be turning up in season two — and it's easy to see why. They're two more of a seemingly endless succession of repugnant Freys, and their presence at Winterfell is annoying but seldom adds to the story. Although one of them does get himself bitten by Shaggydog, which is a plus.
7. Thoren Smallwood
He's a man of the Night's Watch, who becomes commander of the Rangers after the old commander is killed. The show already passed up a few chances to show him — for example, he tries to convince Jeon Mormont to let him lead the expedition beyond the Wall. But Lord Mormont insists on leading the Ranging personally — a decision that's already been taken at the end of the first season. Thoren later argues with Lord Mormont in favor of attacking the Wildlings, eventually persuading him. The fact that we haven't seen Thoren yet means we probably won't.
And now for a few more radical suggestions, which I freely admit may be going too far...
8. Vargo Hoat.
Almost all of the monstrous acts that Vargo Hoat commits in A Clash of Kings could easily be deleted or reassigned to the equally horrible Roose Bolton and his son Ramsay. And even if you keep Vargo as Roose Bolton's right-hand man, you don't necessarily need the complicated subplot in which Vargo is working for Tywin Lannister but then changes sides and hands Harrenhal over to Roose Bolton, with the help of Northmen who are pretending to be captives. There's a lot of "wheels within wheels" going on there. True, the threat of being left alone with Vargo is what finally scares Arya into fleeing Harrenhal. But she has plenty of other incentives to run away by that point, after all the other horrors she's witnessed. (And yes, Vargo commits one very important brutality in the third book — but there are plenty of ways around that.)
9. Aeron Greyjoy
While we're committing blasphemy, let's propose another fairly crucial character for deletion: the man who's so awesome, they named an office chair after him. I love Aeron, and he does play a more important role in later books — but the fact remains that there are too many Greyjoys. Aeron is Theon Greyjoy's loony uncle who nearly drowned and now has become a fundamentalist for the Drowned God. He helps Theon do some reaving along the coastline, as a diversion while Theon's father and sister attack the North. And then he's left behind, while Theon goes off to attack Winterfell. Aeron's fanatical worship of the Drowned God does give us another religion, to add to the Old Gods, the Seven and R'hllor, which is a plus. But all of his major scenes in this book, where he tells Theon that the Iron Men won't accept him as their prince after so long away, could be given to Dagmer Cleftjaw, who's prettier.
10. Craster
Okay, now here's the ultimate blasphemy. I know, I know — Craster is awesome. He's the lovable old psychopath who marries his own daughters and murders his own infant sons. He lives in Craster's Keep, pretending to be a Lord and harboring the Night's Watch in return for a new axe. Any man who touches one of Craster's daughter-wives loses a hand. I pretty much love Craster. But the soujourn at Craster's Keep is just one stop of many on the Night's Watch's tour of the frozen North. There's also the stay at the Fist of the First Men, and then Jon Snow's mission with Qhorin Halfhand, with its tragic end. Craster is pretty much just local color — except for his daughter Gilly, who forms a bond with Samwell Tarly. The stories of Jon Snow and Samwell Tarly would be considerably less entertaining without Craster in the mix, but it would be one way to simplify things quite a bit.