The penny costs 2.4 cents to produce and indirectly diverts resources driving up the cost of production for the nickel to over twice its value.
Minting of the U.S. half-penny was discontinued in 1857 because it was viewed as having too insignificant purchasing power and wasteful to continue minting. Adjusted for inflation it would be worth more than the penny, nickel, and dime today.
The 1 yen coin can be used as a weight, because it weighs exactly one gram. Also, it can float on water.