Below are a collection of "not necessarily highly researched" days which appear to be in some way cocktail/drink related. It also includes dates of "notable historic importance" which may provide a reason to celebrate as well. We will try to add and update to this list when additional dates, or additional information comes to light.
January: National Hot Tea Month
Last Week of January: National Irish Coffee Week
January 1: Bloody Mary Day (#1)
January 11: National Hot Toddy Day
January 16, 1920: American Prohibition began
January 17: National Hot Buttered Rum Day
January 19: Champagne Day
January 24, 1935: The Beer Can was introduced
January 25: Robbie Burns Day
January 25: National Irish Coffee Day
January 31: National Brandy Alexander Day
First Saturday of February: Pisco Sour Day - The National Day of Pisco Sour is celebrated every first Saturday of February, according to a resolution of the Ministry of Production published in 2004. Before that, it was celebrated on February 8th.
February 4: 1862 - Facundo Bacardi Masso, and his brother Jose, bought the Santiago de Cuba distillery and started making rum.
February 7: National Hangover Awareness Day
February 10, 1945: Rum and Coca Cola by Andrews Sisters hits #1
February 11: Don't Cry Over Split Milk Day
February 17: National Café Au Lait Day
February 18: Drink Wine Day
February 22: National Margarita Day
February 22: Don Beach's Birthday
February 27: National Kahlua Day
March 1: Beer Day (in Iceland) - March 1, 1989 is when the 74 year prohibition of beer ended in Iceland. This apparently is a well-celebrated holiday there.
March 3: National Mulled Wine Day
March 3: Bottled-In-Bond Day - In 1897, the US government passed the Bottled-In-Bond law.
March 4, 1634: First tavern in U.S. opens
March 16: Bock Beer Day
March 17: St. Patrick's Day
March 17: National Green Beer Day
March 20: Bock Beer Day
March 27, 1860: The corkscrew is patented.
April 8: Milk in Glass Bottles Day
April 9: Gin & Tonic Day (USA)
April 15: Income Tax Day (also Accountant's Day)
April 16: Kingsley Amis' Birthday (1922) Gravesite reads "supreme clubman, boozer and blimp."
April 19: Alcohol Content allowed on labels (1955)
April 26: National Pretzel Day - celebrate this one with a beer
May: National Egg Month
Second Week of May: American Craft Beer Week
Second Week of May: World Cocktail Week (Designated by The Museum of the American Cocktail)
May 4: National Homebrew Day
May 4: National Orange Juice Day
May 4: Bourbon Whiskey Defined (1964)
May 5: Cinco de Mayo
May 6: Beverage Day
May 6-13: World Cocktail Week
May 8: "Have A Coke" day
May 13: World Cocktail Day: The word "cocktail" is first defined in print (1806)
May 16: Charles Hires invents Root Beer (1866)
May 20: Last episode of "Cheers" airs (1993)
May 25: National Wine Day
May 28: Ian Fleming's Birthday (1908)
May 30: National Mint Julep Day
June: National Ice Tea Month
June: National Dairy Lovers Month
June 1, 1494: Scotch Whiskey Day (as declared by the Chanticleer Society) - Friar John Cor was recorded on June 1, 1494 as procuring supplies for the making of copious amounts of whisky for his Majesty, King James the IV. Not particularly an event of note excepting that this is the first known recorded use of the word whiskey and indicatory of a healthy and long established tradition of distilling whisky in Great Briton, else wise he'd not been making 1500 bottles of the stuff.
- "To Friar John Cor, by order of the King, to make aqua vitae VIII bolls of malt." - Exchequer Rolls 1494-95, Vol x, p. 487.
June 4: National Cognac Day
June 7, 1917: Dean Martin is born
June 8, 1751: Vodka Day (as declared by the Chanticleer Society) The first written usage of the word vodka in an official Russian document in its modern meaning is dated by the decree of Empress Elizabeth of June 8, 1751, which regulated the ownership of vodka distilleries.
June 10: Iced Tea Day
June 12, 1744: Cachaca Day
- "The SBC (Sociedade Brasileira da Cachaça) wants to declare June 12 the International Day of Cachaça because June 12, 1744, Portugal, then colonizer of Brazil, prohibited the production and distribution of cachaça in the country."
June 19: National Martini Day
June 20: Ice Cream Soda Day
June 21: John Lermayer Day
June 27: National Orange Blossom Day
June 30: National Ice Cream Soda Day
July 2: National Anisette Day
July 10: National Pina Colada Day
July 14: National Grand Marnier Day
July 19: National Daiquiri Day
July 24: National Tequila Day
July 26: National Coffee Milkshake Day
July 27: National Scotch Day
August 2: Peter O'Toole's Birthday (1932)
August 4: Champagne is "said" to have been invented by Dom Perignon on this day in 1693.
- It was said that upon his first taste of his sparkling champagne wine he announced "Come quickly, I am drinking stars!". However sparkling wine was known before this time, one possible originator was Christopher Merret, who published in 1662 an account of making wines "brisk and sparkling" by adding sugars to them. Dom's quote is probably also more marketing than actual fact, since its first appearance is in a print advertisement in the late 19th century. This should not undermine Dom Perignon's value to the history of Champagne, because he did work tirelessly on advancing and perfecting the art, and almost certainly the product we drink today owes more than a small debt to his efforts.
August 5: International Beer Day - Apparently "first celebrated" on August 5th, 2007, and henceforth christened.
- "On the night in question, we were beerstorming (drinking lots of beer in an effort to come up with brilliant ideas) band names for a friend's new band, but a couple of hours into the evening, talk turned to how wonderful beerstorming itself was. After thoroughly discussing beerstorming's merits someone declared that there should be a beer holiday."
August 6: Root Beer Float Day
August 9: Diet Coke introduced (1982)
August 16: National Rum Day
August 20: Lemonade Day
August 29: National Whisky Sour Day
August 29: Lemon Juice Day
August 30: Mai Tai Day (as per the Trader Vic Company)
September: California Wine Month
September 2: Beer & Can Day
September 12: Chocolate Milkshake Day
September 15: National Crème de Menthe Day
September 19: Talk like a Pirate Day
September 20: National Rum Punch Day
September 21: Dale DeGroff's Birthday
September 27: National Chocolate Milk Day
September 28: Drink Beer Day
September 29: National Coffee Day
September 30: National Mulled Cider Day
October: American Beer Week (2nd week)
October 1: Sake Day (Nihonshu no Hi) 
October 4: National Vodka Day
October 5: Bloody Mary Day (#2)
- Legend has it the world's first Bloody Mary was shaken precisely 75 years ago, on October 5, 1934-just five years after the invention of canned tomato juice-at the King Cole Bar in the St. Regis, the now-100-year-old beaux arts hotel founded by John Jacob Astor at the eminently exclusive corner of Fifth Avenue and 55th Street.
October 7: National Frappe Day
October 11: World Egg Day
October 12: First Oktoberfest Celebrated (1810) - it was actually a party to celebrate the wedding of Crown Prince Ludwig and Therese of Saxony-Hildburghausen. [http://en.wikipedia.org/wiki/Oktoberfest}
October 16: National Liqueur Day
October 19: International Gin & Tonic Day - appears to have been honorarily declared in 2010 in honour of Mary Edith Keyburn, by her family. It is said she loved to have the occasional tipple of gin and tonic, and passed away on October 19th, 2010 - at the age of 95 - in the hospital with a gin and tonic at her side. It was smuggled into the hospital in a water bottle and served in a teacup. 
apparently was first declared in 2010. In the US, it is also celebrated on April 9th.
October 20: National Brandied Fruit Day
October 27: American Beer Day
October 30, 1830: Birth of Jerry Thomas.
November: National Pomegranate Month
November 8: Harvey Wallbanger Day
November 24: National Espresso Day
December: National Egg Nog Month
Second Week of December: Lager Beer Week
December 1: Bloody Mary Day (#3)
December 10: National Lager Day
December 13: National Cocoa Day
December 14, 1885: Death of Jerry Thomas.
December 17, 1773: The Boston Tea Party 
December 20: National Sangria Day
December 24: National Eggnog Day
December 30: National Bicarbonate Of Soda Day
December 31: National Champagne Day
May 6: National Coffee Day
May 24: National Coffee Day in Brazil
July 22: Coffee Week
July 24: Coffee Day
August: National Coffee Month
September 12: National Coffee Day in Costa Rica
September 19: National Coffee Day in Ireland
September 29: National Coffee Day
October 1: National Coffee Day in Japan
November 24: National Espresso Day
December 26: Coffee Percolator Day