: : Well, this is my surmising, but it may be due to his immense age.

: : Not being quite as good with dates as some others, I am not sure just how much older Cirdan would be, but he is certainly the oldest elf we know about in Middle-Earth. He never really bathed in the light of the trees, which means that he would be pretty weary of Middle-Earth by the Third age. This could be why he looks so old, and has a beard.

: : The next oldest elf in my humble opinion would be Galadriel. However, she spend much of her time in Aman, so maybe she hasn't aged nearly as much. Elrond by comparison is a mere stripling.

: Cirdan may have awoken at Cuivienen (though I couldn't confirm this). Galadrial was born in the Year of the Trees, but there's no real way to tell how old that makes her since her father, Finarfin was also born in the Year of the Trees along with many others. Elrond was born in 540 First Age.

: -RR

Well, Cirdan was indeed ancient at the end of the Third Age, and Elves do age very slowly, hence the white beard - after several millenia, it is the fate of the elves to 'fade' - and become nothing more than spirit. Cirdan is the oldest elf we know of in Tolkeins storys. PoME gives some interesting insights into the bearded one - he was the kin of Thingol and the chief of those that remained behind to search for him. He also desired to go to Aman before Thingol reappeared and decided to make a magnificent ship to carry him over the ocean, but Ulmo came to him and told him that the building of that ship must wait - he in fact was the tutor of Earendil in the ways of ships and helped him to build Vingilot, the star ship.
It became his fate to guard the havens until 'the last ship sails', which I interpret to mean the end of the Third Age - in the Silmaril Cirdan tells Gandalf he will wait for him at the Havens until the last ship sails then 'White was that ship.... and long it awaited the end of which Cirdan had spoken....'
I believe 'The last ship' refers to the last ship of the age, which carries the last of the Noldor from Middle-Earth and ends the Eldar influence in M-E affairs, and I believe Cirdan was on the ship - there is no purpose in his remaining in Middle-Earth after this time. IMHO
Don Q