Sorry, I know this thread is an old one, but I was wondering this recently, searched and found this thread, and just have to put my two cents in!
From what you've all said, and from my own reading of Tolkien's work, my opinion is that Elves actually have two types of sleep:
1) the eyes-open, "half-your-brain-is-asleep", type, that Legolas talks about -- more akin to meditation than sleep. Although they do dream. And, even before I read all this, dolphins came to my mind, too. lol But, I don't care how immortal you are, simple physiology kicks in, and all living beings need:
2) deep sleep. Eyes are shut, body is at rest. Perhaps they normall do the light kind of sleep, and only need deep sleep so often. (an hour a week? a month? pure speculation!
)
For the record, humans have many different levels of sleep, as well! There are three, if I remember correctly -- light sleep, REM (rapid eye movement, when you dream), and deep sleep. Perhaps it's the same with Elves, but with only two types, and they choose which one they will do (unlike humans, who go between all three several times a night!)
Sorry if I rambled! It's late, and I'm tired!