First from Neatorama, a list of Fun and Unusual Units of Measurements
Some of these are just plain silly, but there are a few legitimate chemistry-related units too, including Avogadro's number, Scoville heat units, and alcohol proof.
And also by way of Neatorama, a link to some Molecules with Silly of Unusual Names
These are all actual molecules, although some of the names might be considered more like nick-names (i.e. not the systematic, or most commonly used common names.)
I rather like penguinone - a ketone that looks vaguely like a penguin. I'll have to share it with my daughter who is currently fixated on Club Penguin.