What is Mole Day? "Mole Day is an unofficial holiday celebrated among chemists in North America on October 23, between 6:02 AM and 6:02 PM, making the date 6:02 10/23 in the American style of writing dates. The time and date are derived from the Avogadro constant, which is approximately 6.022×1023, defining the number of particles (atoms or molecules) in a mole, one of the seven base SI units."

The History of 6.02 x 10^ 23 molecules
Question: What is the historical reference on the origin of Avogadro's number? How was it first determined?
Answer: Avogadro proposed his hypothesis in 1811. At that time there was no data at all on the number of particles in a mole, or an agreement on any atomic weights or the standard. The first measurements which could give an approximate value for Avogadro's number were observations of brownian motion by Robert Brown in 1827. Cannizarro (1860) used the Avogadro's hypothesis to develop a defensible set of atomic weights based on 1/16 of the atomic weight of oxygen. This was the basis for progressively more accurate estimates for Avogadro's number over the next 100 years. Reasonable values were available in the late 1800's from sedimentation equilibria of colloidal particles. Millikan's oil drop experiment in the early 1900's gave improved accuracy and was cited in most chemistry text books 50 years ago. Text books in 1958 gave Avogadro's number as 6.02 times 10 to the 23rd. The current value is 6.022137 times 10 to the 23rd.
(The answer to the above question was supplied by Reed Howard, Department of Chemistry and Biochemistry, Montana State University.)

Mole Day Jokes (found on the Web)

Q: How does Avogadro write to his friends?
A: By e-mole!

Q: Why is Avogadro so rich?
A: He's a multi-mole-ionare!

Q: What does Avogadro put in his hot chocolate?
A: Marsh-mole-ows!

Q: Why does Avogadro like Cindy Crawford?
A: She's his favorite super-mole-dle (and she has a mole).

Q: What did the generous mole say when his friends crashed his party?
A: The mole the merrier!

Q: What is a mole's favorite television show?
A: Molerose place

Q: What is Avogadro's favorite day of the week?
A: Moleday

Q: What are mammoles?
A: Four-legged animoles!

Q: How would you describe a stinky chemist?
A: Mole-odorous

Q: Which tooth did Avogadro have pulled?
A: One of his molars.

Q: What did one mole say to the other?
A: We make great chemistry together.

Q: What kind of test do student moles like best?
A: Mole-tiple choice.

Q: Why did Avogadro stop going to a chiropractor on October 24th?
A: He was only tense to the 23rd.

source: http://www.greece.k12.ny.us/oly/science/chemistry/sci_mole.htm