While reading this thread, it got me thinking about not-so-common holidays you celebrate. (Define “not common” how you want to.) There are two holidays my coworkers celebrate:
Pi Day (March 14)–yes, we eat just pie
Shrove Tuesday (the English version of Mardi Gras)–we go out to eat pancakes. Never mind none of us are English or Anglican, we just like pancakes.
What are yours?
I have a beach towel in one of my desk drawers at work, and have been known to hang it over the wall of my cubicle in observation of Towel Day.
Like you, we celebrate Pi Day. We have pie at 3:14 in the afternoon. We also have a lot of fun with Talk Like a Pirate Day.
All the solstices and equinoxes.
May Day (for radicals and communists)
The birthdays of Buster Keaton and Lillian Gish (October 5 and 14, respectively). Just because early October is my favorite time of the year.
Robbie Burns Day.
It’s pretty popular around here.
Is it celebrated in the US?
Shrove Tuesday and Reformation Day but I’m a very active Lutheran. On the latter I enjoy telling everyone “Martin Luther says Yo” and give a “power fist”.
I have also celebrated every (motorcycle) Ride To Work Day since it started. Even the first handful of years when I wasn’t riding as a rule because of my stroke, that one day the bike came out for a run to where-ever I was employed at the time.
I try to treat myself special on Middle Child Day. This year I got a chocolate fudge brownie sundae.
For a long time, I aways threw a Leap Day Party. Haven’t done that in awhile, though.
Star Wars Day (May the Fourth Be With You), and Talk Like a Pirate Day.
I celebrate Snake Whacking Day. Luckily it corresponds with my birthday (May 10).
You only get to do it on your birthday? 
Defining what’s a “common” holiday really does take some, uh, finesse. They nearly all happen once a year, so what makes one more uncommon that the next?
All the solstices and equinoxes, taken together, are actually more common, seeing as how they happen four times a year.
For an UN-common holiday, how about the biblical Jubilee – once every 50 years!
And if New Year’s Day is a holiday, then how about New Century Day (every 100 years) or New Millenium Day (every 1000 years) – and to think, a substantial number of people now alive actually lived to see one of those!
ETA:
See, he’s on the right track there.
Generally speaking we are a bunch of Philistines here in the US, but my pal Jimmy Boland and I did take each other’s photos at the Bobby Burns statue in Winthrop Square here in Boston.
My husband and his idiot friends used to get smashed celebrating Ballintine’s Day.
One year they even had shirts made up!
(They eventually grew out of it…after 50!)
One of my professors celebrated the day the first atom bomb was dropped (he was getting shipped over to the far east pretty soon apparently).
Given this is a US board, I’ll offer Mid-Autumn Festival, now that I’m back home and have a Chinese wife. Add Spring Festival to that, too. The thing is, these are usually multiple day affairs, so I’m still not sure which specific day is “the day,” but my wife lets me know.
My daughter was born on Festivus so it’s a pretty big deal around here.
How does she do on feats of strenght?
I put out a study aluminum pole in the front yard with a christmas bow on it for a few years. I always wondered if anybody got it.
International Tabletop Day
My wife celebrates Buzzard’s Day, when the buzzards return to Hinckley, Ohio. It was a bit of geeky fun for her and a buddy when they were in high school, and she still acknowledges the day.
I like to celebrate Pi Day with a deep dish pizza. And on or around November 7th is usually when I begin my not-quite-yearly playthrough of the Mass Effect series.