The Scouring of the Shire was apperently never shot, and so will not be in the extended edition. The conversation between Saruman and Gandalf at Isengard will be in the EE though, so at least the Saruman/Grima storyline gets tied up a bit.
The Houses of Healing, where we see the interaction between Eowyn and Faramir WAS apparently shot, so we will probably see some of that in the EE.
Hmm.. I think the moment that got me most was when Eowyn was hiding her eyes as her father Theoden was riding down the line of the Rohirrim, spurring his tropps to battle. On his third cry she couldn't couldn't the emotion any longer and let out her own battle-cry, oblivious to who might hear. That cry contained the essence of her character in it: that she was determined to defend her own even if her own people stood in her way. To me that was the most intense moment of the film.