I was listening to the Skeptics' Guide to the Universe today and the first thing they talked about was Captain Picard Day. This refers to an episode of Star Trek: The Next Generation in which there is an annual event to celebrate the ship's Captain, Jean-Luc Picard. Since the episode occurs on stardate 47457.1, this was used as a basis to determine the calendar date. If you know anything about stardates, you know that there is no reliable way to convert between stardates and calendar dates, although there are a number of different formulas used by trekkers.
Apparently, someone calculated this stardate to correspond with 2370 June 16 (186850), so every June 16 is Captain Picard Day. Of course, someone else figured it is November 4 (186991), while others apparently go by the television air date on 1994 January 10 (49362). There are plenty of other possibilities, e.g. March 11 (186754). Plus, the stardate was given later in the episode, and probably refers to a date several days after Captain Picard Day.
If we accept, as most do, that there are 1000 stardates in a year, and that 47xxx represents one year, then 47457 is 45.7% from the beginning of that year, or about 167 days. If the stardate year starts on January 1 and 47xxx represents 2370, then day 167 would be June 16. Of course, this contradicts some references in various episodes, so the stardate year may begin on some other date of the calendar. For instance, 54868.6 must take place on 2378 April 6 (189702), suggesting that 47000 is 2369 September 10 (186572). There are some who even dispute that 1000 stardates are exactly one year long.
At the risk of sparking a holy war, I would say that since it's all bullshit, it does not matter what date we pick. Happy Captain Picard Day!