There have been some excellent quotes in this thread.
"Am I so beautiful you have no words left?" - Midna. I just loved that line. The first time Link sees Midna in her true form, he genuinely does look speechless (which is a hard task for a guy who never really talks). Midna and Link develop such a close relationship throughout the game, I was a kinda disappoint she didn't kiss him before going back through the Mirror of Twilight.
"My country lay within a vast desert. When the sun rose into the sky, a burning wind punished my lands, searing the world. And when the moon climbed into the dark of night, a frigid gale pierced our homes. No matter when it came, the wind carried the same thing... Death. But the winds that blew across the green fields of Hyrule brought something other than suffering and ruin. I coveted that wind, I suppose." - Ganondorf. As has been said in the thread before, this really added a whole layer of depth to Ganondorf and revealed his motivations were much more than simply a lust for power.
"Heh... You know, I've never actually seen you wearing a cap until now! It suits you, little hero." - Ezlo. I always loved this quote. Ezlo is one of my favourite characters from the series and it seemed almost strange to think he didn't know what Link looked like with a cap, since Ezlo was his cap. But he wouldn't know for that exact reason. It was almost the perfect way for them to part ways at the end of the adventure.
"WHOA! B-birds? TINY birds?! Wh-what... ARE they?! And what's with all these trees? There are so many!" - Groose. How can you talk about memorable quotes and not mention Groose? This one had me in fits of laughter. You just get such a sense that he's totally overwhelmed with the new world he finds himself in, that something so normal as small birds and trees are terrifying ideas to him.
"You've met with a terrible fate, haven't you?" - Happy Mask Salesman. This is perhaps my favourite quote in the whole series. The first time he says it, it's really just a statement of fact. You have met with a terrible fate, having been turned into a Deku Scrub. When you see it after the moon hits, just before you resume from the Clock Tower, it takes on much deeper significance. First, it refers back to that orignal meeting, indicating that you've somehow gone back to the start of the 3-day cycle. Second, since it shows up on the black screen and you hear his little laugh, it implies the Salesman has something to do with it. Coupled with the fact that he seems to know the fate that is to befall Termina and exactly when it's going to happen, the mystery surrounding his character was enhanced so much by that simple phrase. 8 words have never made me ask as many questions before, or made me both respect and fear a seemingly innocent man. This quote is one of the first things that instantly pops into my mind whenever I think of Majora's Mask or indeed, the Zelda franchise.