Do elves sleep?

Well, why shouldn't they? :)

They can dream but they don't sleep. Instead they sort of meditate.

Sort of, but not in the way humans do. Elves rest by looking at beautiful things to refresh their minds, or providing themselves with 'waking-dreams' of beautiful things. They don't close their eyes, but their eyes glaze over. A sleeping elf would look like a human gazing into the middle distance.
They also don't need to sleep as much as humans do. I think an elf could last without his waking-sleep for a few days, but this might cause some discomfort.

actually, in chapter VI of book three (two towers), the first paragraph first page, it says "Legolas and Gimli slept; Aragorn lay on his back"
Elves do sleep :)

I sincerely hope they do. They are elves, not Cullens. I have read fanfictions which imply otherwise, but I think the idea is ridiculous. Elves must sleep.

Yup, I assume so.

They sleep. Grant it, they may not sleep very much, but they do sleep.

Yesssssssssss

no they dont