My two most favourite moments were 1) when Matt took on both Galad and Gawyn with a quarter staff in Tarvalon, and beat them despite still being very weak from his healing from the dagger from Shadar Logoth.
2) When Rand pays a visit to Egwene in the white tower when she is Amyrlin. He pretty much calmly walks into the lions mouth surrounded by Aes Sedia and then calmly walks out again with no one even trying to stop him.
I liked Egwene and Elaida's dinner scene. That one was AESOME!
I also liked the scene when Mat and Perrin catch Rand with the Dragon banner during TGH.
All in all TGH is my favorite book. So many great scenes.
Yeah. The whole concept of them chasing after something is really cool. And the fight with Turak at the end and when Ingtar has his last talk with Rand. All great.
Some of my favorite parts are the scenes involving the snakes and the foxes, they're just so interesting and mysterious! Also any scene with Mat, gotta love that little scamp
I love the scene where Elayne, Brigitte, the Kin, Sea Folk, etc. are escaping the Seanchan through a gateway. Elayne is trying to unravel her weave while hurt and Brigitte is firing off arrows like a madwoman.
I also love the Egwene and Elaida dinner scene. Love reading about Elaid being carried off by the Seanchan too
Oh and there's the first-sister ceremony between Elayne and Aviendha.
And I like Egwene being summoned to the Little Tower...especially when I re-read because I know what's coming
Outside of the scenes already mentioned, all of which are awesome scenes (especially the one with Rand at the end of TGS), I think for me my favorite scene is the very last one... with Rand riding away, nobody knowing he still lives, puffing away on his pipe (that I'm not sure how he lit)... it just has a final feel to it; it's a bit cheesy but it really made me come to the realization that after over a decade of reading it's finally over :'(
My favorite moment, from what I can immediately remember, is anything Egwene did to stand up to Elaida in TGS. I mean, friggin' a, woman, you are remarkable.