My favorite scene involving Moiraine is when she takes Lanfear out through the ter'angreal doorframe in The Fires of Heaven. Pretty heroic.

My favorite memory of Lan is when Moiraine falls through the red arch and dies/disappears.

I have to go with Lan teaching Rand what to say to the Amyrlin in TGH. And Moiraine's reaction afterward.

Also, in tEotW, Rand's reaction to finding himself dancing with Moiraine. And Lan's reaction to hearing that Nynaeve followed the trail he had left.

Also, every other scene... :)

My favorite Lan and Moiraine moment, hmm? Though the docks of Cairhien is hard to beat as a Moiraine moment, I would say that my favorite of them together is in TEOTW Chapter 41 'Old Friends and New Threats' where Mat is in his and Rand's room at The Queen's Blessing. Moiraine touched his knee and he slashed at her with the dagger.

'One minute Lan was in the doorway, and the next he was at the bedside, as if he had not bothered with the intervening space. His hand caught Mat's wrist, stopping the slash as if it had struck stone. Still Mat held himself in that tight ball. Only the hand with the dagger tried to move, straining against the Warders' implacable grip. Mat's eyes never left Moiraine, and they burned with hate.

Moiriane also did not move. She did not flinch from the blade only inches from her face, as she had not when he first struck.'

Any description of this scene other than the actual quote from the book doesn't do its awesomeness justice.

My Favorite and worst memory was when Moiraine tackles Lanfear through the red archway.

My favorite scene with both, is the end of New Spring when Moiraine bonds Lan.

"Handing her Arrow's reins, he said, "Where do we ride first?"

"Back to Chachin," she admitted. "And then Arafel, and. . ." So few names remained that were easy to find. "The world, if need be. We win this battle, or the world dies." Side by side they rode down the heal and turned south. Behind them the sky rumbled and turned black. Another late storm rolling down from the Blight ."

I think its hands down, the night by the lake when Lan and Moiraine first meet! Oh man nothing can compare to my own imagination for the thought of Lan's face when the water stops blasting him.....lol! The writing was great and the New Spring really gave so much to the rest of the series.

My favorite memory of Moiraine is when she tags on as Rand's advisor, and slowly but surely became the first Aes Sedai I liked in the books.

Lan, I will always remember for his sparring with Rand up in, I think, Shienar, and just giving him some great words of encouragement and wisdom.

There are such a lot of great scenes with both and each of them separately that it is hard to pick just one (each).

When Moiraine suddenly stripped naked to go down to Rhuidean is one of my favorite Moiraine moments. What a surprise! And it is so sparsely written as to be rather mysterious as it occurs.

I loved Lan telling Rand to assume "Cat Crosses the Courtyard" as he walks him back to meet the Amyrlin Siuan.

One of my very favorite Lan scenes is his dive and save of Nynaeve in the sinking boat--having arrived just in the knick of time TO save her. That was rather astounding.

Lan prepping Rand for his audience with the Amylrin Siuan Sanche at the beginning of TGH. It is as though Lan treats Rand as a younger sibling about to step onto the path of manhood/warrior:

1. Dressing Rand in a heron collared shirt, and giving him a golden cord complicated knot and a Manetheren pin.

2. Telling him -- "You kneel when you go before her. One knee only, mind. You're not some merchant caught giving short weight."

3. Having Rand walk into the audience in the stance of "Cat Crosses the Courtyard" -- "It was a relaxed, almost arrogant, saunter."

My favorite scene, hands down, is Moiraine's test. For years, I'd been a part of a roleplaying site, set in the Tower, and we could only imagine what the test was like. That opened up so many doors and ideas in our minds. The book as a whole helped shape our view of Accepted culture under more normal circumstances than the main series, as well as newly-raised Aes Sedai cultureshock, but more than anything it was the test itself that fired our imaginations.