Thursday
According to The Hitchhiker's Guide to the Galaxy, the Earth is destroyed on a Thursday, and the only survivor from Earth on the day of destruction is a one Arthur Dent, who happens to be wearing a dressing gown. He is saved by his friend, Ford Prefect, an alien who knows how to hitchhike throughout the galaxy, etc.
Lancaster
Hence, each Thursday, CTYers wear bathrobes all day, for fear that the world might end. Those who don't have bathrobes carry towels, the most useful item an intergalactic hitchhiker can have. Those who do have bathrobes bring towels anyway.
Also, many CTYers refer to the last Friday of camp as Thursday since the CTY (which is the world) both end. The last two days are switched at Lancaster (i.e., Monday, Tuesday, Wednesday, Friday, Thursday). This is also sensible in the fact that the dance now occurs on a Friday; we can't have dances on Thursdays.
Some have taken to calling Thursdays "Bathrobe Day;" however, most people understand that you just can't not have a towel or bathrobe on said day.
Bathrobes
At Lancaster, those who do not wear their bathrobes on are said to be "naked."
I believe this started with Dennis, and it was a Douglas Adams/Hitchhiker's Guide reference. Dennis had a wonderful Dennis-colored (blue-green) bathrobe that he would wear on Thursdays. Not sure how far back this goes--at least to LAN.95.2.
--Aurora 16:14, 12 Nov 2004 (CST)
To follow up on Aurora's comment: The Dennis she referenced is famed CTYer Dennis Clark.
A particularly striking bathrobe story concerns B-B Stern, who attended Lancaster in the late 1990's and early 2000's. B-B apparently wore his bathrobe to school during the rest of the year as well, and the tradition was adopted by a friend of his, Sean Treanor, who had not attended CTY. Sean then continued to wear his bathrobe even after B-B had transferred to a different school. It is unknown whether the bathrobe tradition has spread anywhere else outside of CTY.
--Sammka 21:19, 27 August 2006 (MST)
The biggest Hoopy Froods wear British bathrobes (LAN).
Carlisle
At Carlisle, towels and bathrobes are only worn on the last Thursday, called "End of the World Day."
"As far as I know, this has been around at Carlisle since well before '95. It was originally called "towel day" due to Ford Prefect always carrying a towel with him (and the million other significances towels have to the hitchhiker's guide). Towels were worn in numerous creative manners. At some point, some people combined it with bathrobes (these people couldn't cope with towels), and so it is referred to as "towel/bathrobe day" or sometimes (sadly) just 'bathrobe day.'"
--SomnusLupus 28 Nov 2004
Also, every Thursday you are offered free high-fives becuse every Thursday is free high-five Thursday!
Saratoga Springs
See Carlisle.