What, no Caspar?
My favorite (introduced to me here, I think) is the blue jay emetic unit, used to measure the quantity of cardenolides in plants, extracts, and butterflies.
I like some of the others listed there:
Bovate, the amount of land one ox can plough in a single year (also called an oxgate). Approximately 15 acres or one eighth of a carucate.
Virgate. the amount of land a pair of oxen can plough in a single year. Approximately 30 acres (also called yard land).
Carucate. an area equal to that which can be ploughed by one eight-oxen team in a single year (also called a plough or carve). Approximately 120 acres.
My only problem with this definition is the term ‘jiffy’ has been around since the 1600s, which is before there were fermis or anyone though light wasn’t instantaneous.
My contribution to units: the hoover - the unit of suck.
“The boss said I have to come in on Saturday”
“Oh dude! That’s gotta be three hoovers!”
I’ve always been fond of a unit of measure I first saw in the comic strip Schlock Mercenary - the Hurtz Scale, which defines how painful certain things are.
A different webcomic introduced me to the concept of the “Imperial Assload” - which very frequently describes the amount of work on my desk in a given day…
I’m slightly astonished that this hasn’t been posted yet: Giraffe.
Google says that 1 newton is approximately 1.145 stone-furlongs per fortnight squared.
Make that 1.145x10^9…
I think we need a name for a new unit of force that is equal to 1 stone-furlong per fortnight squared. How about “Sparrowfart”?
Kellikam: A Klingon unit of distance, roughly equal to two kilometres.
Antipodean unit of the infinitesimally small - the Bee’s Dick. As in, “Holy Crap! That car just missed me by a Bee’s Dick.” Never seen in plural form.
Coat of Varnish - the amount by which a cricket ball missed the stumps, according to disappointed bowlers. “Another coat of varnish and you’d be gone, mate!” Rarely convincing. Comparative size of CoV and BD unknown.
Dutch metric stone, right?
The Pyramid inch, “a God-given measure handed down through the centuries from the time of Shem (Noah’s Son)”, discovered in the 19th century. It allowed all sorts of remarkable facts and accurate prophecies (of events prior to the 19th century) to be encoded into the dimensions of the Egyptian pyramids (given sufficient fudging).
I submit the most useful unusual unit is the “finnagle”, which is the quantity you add, subtract… well, hell, it’s the amount you somehow adjust the quantity you have or measure to make it the quantity you’ve calculated or you’re budgeted for. It goes with drawing the curve first and then adding data points to support and make it a “best fit” curve.
(emphasis added)
Apparently not so:
http://www.washingtonpost.com/wp-dyn/content/article/2005/12/07/AR2005120702328_pf.html
Not to pick a nit (hah!) but isn’t the unit “light-feet” dimensionally inconsistent with time? I assume you mean it to be the speed of light multiplied by a foot, which in dimensional terms is (L / T) * L = L^2 / T.
Surely what you want is the feet-per-light, which would give you L / (L / T) = T.
Also, great username and unit combination!
I’m not sure that in the colloquial names light-nanosecond and light-foot there’s any specific dimensional analysis implied by the form of the names themselves. A light-nanosecond is the distance travelled by light in a nanosecond, and a light-foot* is the time required for light to travel a foot, right?
[sub]*Also a Canadian folk singer.[/sub]
But that’s… that’s inaccurate! Or worse, inconsistent! 
So we should rename the Light-Foot to Gordon!