Night Elves stand approximately 7 feet tall. Using the height comparisons between avatars, and assuming avatars represent a near average height for each gender and race, this puts females at approximately 7 feet tall and males at 7.5 feet tall.
If Night Elves have the same ratio of height variance as humans, then their height can vary within a foot shorter or taller from the average height designated to their gender.
Night Elves tend to be on the athletic side in terms of body type. Assuming Night Elves are not, inch for inch, heavier than a human, one can simply use modern day humans to estimate weight.
Yao Ming (Basket Ball player) stands 7'5 and weighs 310 pounds. Isis (Female wrestler) stands 7'0 and weighs 245 pounds.
Without their immortality, we don't know exactly how long a Night Elf lives. It is said that the Night Elves now share a similar lifespan as their High and Blood Elven cousins.  And while Blood Elf and High Elf age are suspect, it still puts Night Elves far and beyond other Azerothian races.
Night Elf aging also appears to be the same as human aging up to a point, with Shandris Feathermoon being an adolescent during the War of the Ancients and looking the part. As well, children have started 'growing up' on Teldrassil, meaning that within the less 8-10 years since Teldrassil's growth they have matured steadily into teens. Around the Night Elf's 20s to 30s the aging process slows or stops.
Speculation: The first few centuries of a Night Elf’s life are presumably nothing like the first 18 years of a human life. This is inferred because the first few centuries of a Night Elf's life, when they are still considered youth in their society, spans the entire life expectancy of a human twice over. This means that young adulthood for a Night Elf is similar to living two full human lives.
Tyrande Whisperwind was roughly 13,836 during the Warcraft III campaign. Malfurion and Illidan Stormrage were 15,032. Add ten years since that time and that is their present age. 
Night Elf skin tends to come in shades of purple. These can range from dark, such as plum and maroon, to light, such as lavender. It is unknown if Night Elves can 'tan'.
Their skin color has led to the 'slang' term “Purple” in reference to their entire race.
Night Elf hair comes in a variety of colors. These include raven black, midnight blue, light blue, light green, forest green, silver, dark purple and light purple. Female Night Elf Death Knights exhibit pink hair, yet this seems to be tied to their undead state as no living elves show this hair color.
Hair styles are varied. Long and short hair are both unisex, as are ponytails and braids. Females are shown to decorate their hair with tiaras, leaves and feathers. Men sport a wide variety of beards, some being quite thick and Dwarf-like.
Night Elf blood is purple. Because of this, a Night Elf's blush would be very dark, almost maroon or black in color.
Night Elves have heightened senses. Furthermore, they are able to see in the low light situations.
A major power Night Elves have is they are able to detect and sense 'wrongness', corruption and evil, at least in a general area.
Night Elves only have two naturally occurring eye glow colors; amber and silver. A blue glow occurs in Death Knights.
Before the War of the Ancients, amber eyes were considered to be a sign of great power or destiny. After Night Elves started to dabble in druidic magic it was revealed that amber eyes are a sign of druidic potential. It is possible for a Night Elf's eyes to turn from silver to amber after taking up druidic studies.
Night Elves also seem to have some issue with daylight, as they are a nocturnal race. At least once we see Night Elves having to squint during the day to make something out in the distance.
There is a significant difference between ears of a Night Elves and the ears of other elves that we see in World of Warcraft. Where other elves tend to have straight, upward pointing ears, the Night Elves have longer, slightly curved ears that protrude directly toward the back of the head, and often extending beyond. Additionally, we can see from some of the cinematic trailers and videos by Blizzard Entertainment as of the Legion expansion that night elf ears shift and move, and can be expressive.
However, like all elves the Night Elves large ears tend to be greeted with admiration or mockery by other races. 
Art is conflicting in if Night Elves have claws or not. Earlier art portrayed them with long, claw-like nails, yet art (especially after WoW) depicts them without. As of Cataclysm, however, every new or updated Night Elf model, including Azshara, Malfuion, Illidan, and Tyrande, have been displayed with elongated nails.
However, almost all art depicts Night Elves, both male, and female, with sharp, elongated canines.
Recently it has been confirmed that Night Elves evolved from Dark Trolls.
It is unknown if this is known to the race as a whole. Even if it was revealed it may not provide any source of strife as Night Elves believe they are Elune's children. It has been speculated that Elune did have her hand in the Night Elves' creation, given her son, Cenarius', appearance.