Via Symmetry Breaking, I discover the link to Sensible Units, which uses a unique definition of sensible. Type in a distance, and you might get the equivalent in AA batteries end-to-end or Alaskan moose antler spans. Or find a weight in equivalent average housecats.
Then there is the List of unusual units of measurement
It in includes the Sagan, which I used not long a ago, unaware it had already been codified in Wikipedia. There are more mainstream units, such as the barn and the shake.
And then we have the List of humorous units of measurement, including the Smoot mention in the Symmetry Breaking post, and the Helen, a unit of beauty (a milliHelen being the beauty needed to launch a single ship).
Negative values have also been observed—these, of course, are measured by the number of ships sunk or the number of clocks stopped. An alternative interpretation of 1 negative Helen is the amount of negative beauty (i.e. ugliness) that can launch one thousand ships the other way.
I question a few of these. I would think that happiness would be measured in clams rather than puppies, because of the need to quantify not only the warmness and dryness (wet dogs bring forth little happiness) but the calibrations for breed of the dog. I can see arguments breaking out, because a standard Lab generates more happiness than a Schnauzer — lots more — according to my research.
And speaking of dogs, the unit for illness is missing, and how sick you are would be measured in dogs. Health, or rather fitness, would be in fiddles. Insanity (madness) would be in Hatters. Nervousness would be in rocking chairs, calibrated with a standard long-tailed cat in a standard room. Smoothness would have the units of silk. Stubbornness measured in mules, while gentleness is measured in lambs. Uselessness, which surprisingly is quantized, in tits on some standard bull.
I think there are some standards labs that need to get cracking. At 0.6 greased lightnings, if not faster.