The Elves were a far more beautiful race than Men, and generally taller. Among them, those who had gone to Valinor were the fairest and had the greatest skill of body.
There are no explicit references to pointed Elvish ears in The Lord of the Rings or The Silmarillion. It was stated elsewhere that "the Quendian (Elvish) ears were more pointed and leaf-shaped than Human." However, practical considerations, including a number of occasions where Men were mistaken for Elves (most notably Túrin Turambar), suggest that the points must have been subtle.
In the Etymologies Tolkien noted the similarity between the words for "leaf" (lassë, las) and "ears" (lasu, lhaw) and suggested an etymological connection. This indicates that he envisioned their ears as leaf-shaped.
Elven hair colour is quite varied and complex. In general, the Vanyar were golden-haired, and the other Elves (including Noldor, Sindar, and Avari) had dark or even black hair, although some of the Teleri (including Celeborn) had silver hair. Lúthien Tinúviel and her remote descendant Arwen Undómiel, both described as the fairest of all Elves, were dark haired.
This is not the full picture, however: Finarfin, the youngest son of Finwë, and his descendants (such as Galadriel) had golden hair on account of Finwë's second wife, Indis of the Vanyar. Idril, the daughter of Turgon, had golden hair inherited from her mother, Elenwë of the Vanyar. Even the sons of Fëanor, the eldest Noldorin prince, were not all dark-haired: Maedhros and the twins Amrod and Amras had auburn hair, from their grandfather Mahtan. Fëanor's son Celegorm had blond hair, thus his epithet the Fair in contrast to his brother, Caranthir the Dark.
Additionally, a silver hair colour existed in the royal houses of the Sindar, with Thingol and Círdan both described as having silver hair. Galadriel displayed an extremely rare hair colour nowhere else observed: "silver-golden" hair, said to be dazzlingly beautiful ("blending the light of the Two Trees, Telperion and Laurelin"), which may have been a result of her unusual mixed Noldorin-Vanyarin-Telerin heritage (her mother was the niece of Thingol, and her father was a son of Finwë and Indis). Thranduil, father of Legolas and a Sindarin Elf, is described as having blond hair in The Hobbit, but his son Legolas' own hair colour is not recorded.
When Tolkien describes Elven eyes, they tend to be grey. This is certainly true of Lúthien (and her descendants: Elrond, Arwen and her brothers, and Aragorn and the Dúnedain). Voronwë, who guided the man Tuor to Gondolin, also had grey eyes.
Though he was half-Noldorin, Maeglin is said to have dark eyes (possibly from his father Eöl, who was not of the Noldor), while Olwë (the brother of Lúthien's father Thingol, and a Telerin king) had blue eyes. The eye colour of most other Elves is not mentioned, and so would be difficult to generalize.
Because of their (typical) beardlessness and beauty, the Elves are sometimes perceived as androgynous. However, they were probably not meant to be so; Legolas was described in the following way:
"He was tall as a young tree, lithe, immensely strong, able swiftly to draw a great war-bow and shoot down a Nazgûl, endowed with the tremendous vitality of Elvish bodies, so hard and resistant to hurt that he went only in light shoes over rock or through snow, the most tireless of all the Fellowship." (The Book of Lost Tales Volume 2)
Elves apparently did not sleep but rested their minds with beautiful thoughts in reverie or looking at fair things.
Also, unlike Men, Elves were ambidextrous