"As they came to the gates Círdan the Shipwright came forth to greet them. Very tall he was, and his beard was long, and he was grey and old, save that his eyes were keen as stars; and he looked at them and bowed, and said 'All is now ready.'"
-The Lord of the Rings, The Return of the King, The Grey Havens (Book 6, Chapter 9)
So you see, Cirdan was the only elf, as far as I know, who had a beard.
Greetings
Maraelion