There are TONS of puns in Klingon.
The words for aunt and uncle are me' and 'IrneH, 'e'mam and tennuS. (Look at them backwards.)
The word for a drink like root beer is 'awje'. (Think of the noun conjunction je.)
The verbs for using the toes are mar, Hom, roS, nan, and Qay. (Piggies!)
A kind of stringed instrument is a leSpal. (Think of guitars.)
Juice is vIychorgh (what number do you see in there?)
There are many, many more. Some are all but indecipherable. For instance, the word for neighbor is jIl. Marc Okrand had a neighbor named Jill. The words for either end of a long object, megh'an and 'er'In, are named after his twin nieces.