--Brilliant way to start off, unknown world and the read goes to the farthest edge to find danger lurking. Numerous things have importance later (in the book and several books down the road).
Bran I 9/10
--The last surviving character from the Prologue ends up dead and we meet not only the titular POV for the first time, but three more (Eddard, Jon, & Theon) as well. Foreshadowing heavy at the end of the chapter.
Catelyn I 9/10
--The book's main plot first appears; a non-northerner provides more information of the book's current setting as well as on it's future settings.
Daenerys I 9/10
--The beginning of Dany's journey starts here and we learn about the Targs as well as get an inkling about Viserys. It's important to remember that at the beginning Dany thought of the house with the red door as "home".
Eddard I 9/10
--The introduction of other important characters, especially King Robert who's wishes helps spurs the plot (Eddard as Hand and the Joff-Sansa marriage).
Jon I 8/10
--Would have been another 9, but for the inconsistent portrayal of Tyrion.
Catelyn II 7/10
--The "Jon-hate" could have been less over-the-top, the secret note from Lysa could have been read (out loud or mentally by Catelyn) instead of just blurted out. Interesting information that helped the plot, but some things didn't work.
Arya I 8/10
--Meeting the Stark tomboy and what her interests are. Good introductory chapter and nice observations of details.
Bran II 10/10
--A lot of things that happen later in the book and series is as a result of what occurs in this chapter. We learn more about Bran as an individual so that we can understand the loss he'll feel for a while after this chapter. And a shocking reveal...
Tyrion I 9/10
--The Imp makes a big splash when he slaps sense into Joffrey and observes for us the reader the interactions between his siblings.
Jon II 8/10
--The "Jon-hate" makes another appears, but it's not has heavy-handed like from Catelyn's POV though it doesn't make sense (b/c if Jon had been crippled he'd be staying at Winterfell with Catelyn which was not what she'd want). Major character development when it comes to Arya.